If the antinuclear members of the Greater London Council have their way, signs will soon appear at this city's boundaries greeting motorists with this notice: "You are now entering a nuclear-free zone."

The signs would be a symbolic gesture, adding London to a lengthening list of about 120 British cities and counties that declared themselves nuclear-free zones during the past year. Lacking power over the U.S. and British military bases and depots where nuclear weapons are stored, they can do little more than refuse to cooperate with national civil defense planning.

The signs would also be significant new peaks on the chart of the nuclear fever that has hit Western Europe in recent months. Britain's reborn Ban the Bomb movement has campaigned for creation of these local nuclear-free zones as symbols of the much larger and more meaningful design of nuclear disarmament campaigners on the continent. They want to make entire countries and groups of countries nuclear-free zones, ultimately linking them together to form a nuclear-free Europe, "a calm space between the superpowers," in the words of British historian E. P. Thompson.

That idea is powering many of the nationally based disarmament movements that have called hundreds of thousands of antinuclear protesters into the streets of European capitals in the past month. The nuclear pacifists have suddenly become significant political forces in West Germany, the Netherlands, Belgium, Greece, Britain and other countries, and have pushed themselves into the plans and calculations of Secretary of State Alexander M. Haig Jr. and other Reagan administration officials.

They have also attracted the attention of Soviet Communist Party chairman Leonid Brezhnev, who arrives in West Germany next week on an infrequent trip to the West and who can be expected to make his own gestures to capitalize on the nuclear malaise.

Communist and communist-front peace groups are channeling as much of the protest as possible against American rather than Soviet nuclear arms and strategy, and concern is rising in most European governments about the distinct anti-American tone to many of the demonstrations.

But the extensive involvement of church groups and clergy, youth organizations and middle-class, middle-aged citizens committed to democratic values suggests that Brezhnev is plowing in a fertile field, not creating that field through manipulation. The antinuclear movement advances a mix of often vague, sometimes conflicting plans and goals, but the pursuit of nuclear free zones has given it an integrating concept and a form of coherence and moral force in recent weeks that governments must now confront.

And, since Oct. 18, its number apparently includes a NATO member government. On that day, Andreas Papandreou, a socialist, was elected prime minister of Greece. He has served notice since that Greece will demand that the United States remove all nuclear warheads stationed there within a year, as the first step in what a Greek spokesman predicts will be "the denuclearization of the Balkans."

The spreading attraction of nuclear-free politics was also evidenced by the march of 100,000 people in Bucharest Saturday to support Romanian President Nicolae Ceausescu's call last month for withdrawal of Soviet nuclear rockets targeted on Western Europe if NATO will cancel its plans to station new medium-range missiles in five countries. Britain's disarmament forces here have cited Ceausescu's stand and Poland's ability to continue to reject the Soviet Union's demands and pressures on internal affairs, as evidence of a coalescing European political will.

The hopes for a Europe that could be left out of the nuclear politics of Washington and Moscow date back almost to the first detonation of a nuclear device. They were formalized into a plan for Central Europe by Poland's foreign minister, Adam Rapacki, in 1957. But the debate died after France joined Britain in developing an independent nuclear deterrent, which made European nuclear disarmament much more complicated, and after the first moves toward detente produced hopes that binding nuclear treaties between the superpowers would automatically protect Europe.

Interviews in four European NATO capitals during the past two months with rank-and-file members as well as the leadership of the nuclear pacifism movement indicate that a variety of factors contribute to the particularly strong rebirth of the debate. Three seem to stand out:

The political defeat of SALT II in the United States and the Soviet invasion of Afghanistan, bringing about the collapse of detente, have produced a crisis in confidence among Europeans in traditional arms control negotiations, and they are seeking radical departures in disarmament. The Reagan administration's open and deliberate downgrading of arms control as a policy tool has been a major factor in this in recent months.

There is a generation factor. The generation of those in power now in Europe came of age during the heated disarmament debates of the 1950s, as NATO was formed. Many of those in the streets have grown up at some distance from the Cold War and the original Ban the Bomb controversies.

The menace of technology, which helped spark Islamic reaction to Western presence in Iran and elsewhere, is also present in the European response today. Europeans have been made aware that there is a new generation of extremely accurate missiles about to be put into place on their soil to counter greatly improved Soviet rockets already targeted on them.

The technological menace may help explain why the "peace movement" has focused on the planned deployment of 572 Pershing II and Tomahawk ground-launched cruise missiles scheduled to begin in December 1983 as the centerpiece of its campaign. The missiles are intended by the political leadership of NATO -- including the European governments that belong to NATO -- as visible symbols of the alliance's ability and determination to resist Soviet technological advances.

For those leading the campaigns of protest against Soviet and American rockets, the recent successes have confirmed their wish to push on beyond stopping the missiles to "putting together nuclear-free zones that would sweep nuclear weapons out of the continent forever," says E. P. Thompson, who helped found the Campaign for Nuclear Disarmament in 1958 and recently watched it grow once again into a potent force for mobilizing public opinion after nearly two decades of dormancy.

"If the idea is accepted that European nuclear disarmament can be a process of organic growth, greater responsibility for immediate action devolves on each nation," argues another veteran theorist of the European disarmament movement, former Swedish Cabinet minister Alva Myrdal.

Some disarmament campaigners, including Thompson and British Labor Party left-wing leader Tony Benn, want, in the words of the Rev. Bruce Kent, a Roman Catholic priest who serves as general secretary of Britain's Campaign for Nuclear Disarmament, "to start the process of breaking up the superpower blocs" with nuclear-free zones and create a nonaligned Europe with its own independent security arrangements. But others believe Western European nations could and should renounce nuclear weapons while remaining inside NATO.

"We should stay in NATO," argues Lord Hugh Jenkins, national chairman of the Campaign for Nuclear Disarmament, "and take part in a general de-escaluation of nuclear weaponry within the alliance."

The appeal this argument has developed has become a major problem for European governments. In particular, it has helped cause serious rifts in the left-of-center social democratic and labor parties that govern West Germany and Denmark and provide the principal opposition in Britain and Norway. Their membership has become the obvious constituency for the movement

The splintering of Britain's Labor Party by the issue, and other ideological issues, can be seen on the Greater London Council and the battle there to turn London into a symbolic nuclear-free zone. A majority of the Labor Party members ruling the council are advocates of Benn's far-left policies for more militant socialism domestically and unilateral nuclear disarmament internationally. Others in the council's Labor Party majority seek less extreme positions, while a few strongly opposed to the leftists have defected to the new Social Democratic Party.

Benn articulated his vision of a new Europe earlier this year in a speech that endorsed an alternative European security system modeled on the present defense strategies of neutral nations Sweden and Switzerland, which he said were based on "dissuasion" rather than "deterrence." Both countries, he said, "have a large citizen army that can be mobilized very quickly and would inflict immense casualities on any invader, without nuclear weapons or creating a military elite that could organize a domestic coup."

In West Germany, attempts are being made to link the idea of a denuclearized zone with the alliance's military doctrine. Last week, Guenter Gaus, foreign policy advisor to the executive committee of the West German Social Democratic Party and a protege of former chancellor Willy Brandt, called for a return to the doctrine of massive retaliation so that Europe could protect itself exclusively with conventional forces while sheltered by the American nuclear umbrella.

This strategy of massive retaliation -- that is, a strategy in which the United States would launch an all-out nuclear attack on the Soviet Union in response to a Soviet invasion of Europe -- was shelved in the 1960s as the Kennedy administration developed the concept of a graduated and flexible response to Soviet attack. The technological advances made in missilery have raised concern now in Europe that selective targeting will allow both Moscow and Washington to be so flexible that the war will be fought only in Europe.

Gaus' suggestion created a new uproar in West Germany, where he was criticized by the right for being totally unrealistic and by the left for suggesting the peace movement's real aims were to protect Europe from nuclear danger but not to go on to getting the superpowers to lay down their atomic burden as well. The mainstream antinuclear groups say that getting total disarmament is precisely their aim.

While disagreeing on just how and where to begin creating a nuclear-free Europe, leaders and theoreticians of the nuclear disarmament movement see the map of Europe as a patchwork of potential nuclear-free zones:

In the north, they wish to see Norway and Denmark also rule out deployment of nuclear weapons on their territory in wartime and join in a Nordic nuclear-free zone with neutral Sweden and Finland. Such a plan has been championed by recently retired Finnish president Urho Kekkonen since 1963 and was revived earlier this year by leading Labor Party politicians in Norway, but interest in Scandinavia has since cooled.

In the south, Papandreou's pledge to get the United States to remove the largely antiquated force of several hundred warheads for artillery shells and Lance missiles stored there opens the way for Greece to join independently communist Yugoslavia and Albania and Warsaw Pact members Bulgaria and Romania in a Baltic nuclear-free zone proposed by the Bulgarian government immediately after Papandreou's election victory last month. Just northwest of the Balkans are already neutral and nuclear-free Austria and Switzerland.

North of them, Myrdal and others argue, West Germany could join East Germany and Poland in the nuclear-free zone advocated originally by Rapacki. Some versions would also include Hungary and Czechoslovakia. On Germany's western flank are the Netherlands and Belgium, where disarmament campaigners believe they have the best immediate opportunity to prevent basing of the new cruise missiles and to ban NATO battlefield nuclear weapons already stocked in the two countries.

From these components, Myrdal envisions a nuclear-free zone stretching from Lapland to the Greek islands separating the superpower blocs in Europe. Thompson argues that this could "permit smaller nations, East and West, to resume their own initiatives. So that ultimately, this process could take in all of Europe, even Britain and France, who have their own nuclear weapons. Thompson's European nuclear disarmament umbrella group states its objective as removing nuclear weapons from "the entire territory of Europe, from Poland to Portugal."

The Socialist International, which encompasses the Social Democratic and Labor parties of Western Europe and elsewhere, last year formally advocated establishment of nuclear-free zones wherever possible throughout the world as "a feasible method" of reaching "the ultimate goal" of the "elimination of all nuclear weapons." Britain's opposition Labor Party, for example, has committed itself to ridding the country of all British and U.S. nuclear weapons "as Britain's direct contribution to the creation of a European nuclear weapon free zone and as a powerful British initiative in the wider process of nuclear disarmament."

As the antinuclear movement has gained strength, the efforts of far left and communist-front peace groups to get into the action and influence it, have grown.

British communists and members of the extreme-left Socialist Workers' Party are among the national leaders and local organizers of the Campaign for Nuclear Disarmament here, for example. The relatively small West German Communist Party and Communist-linked German Union for Peace are in the forefront of the disarmament movement there. The second secretary of the Soviet Embassy in Copenhagen was recently expelled for participating in meetings of left-wing disarmament groups in Denmark and paying for newspaper advertisements urging opposition to NATO nuclear weapons policies, according to the Danish government.

But Kent and Thompson stress that Britain's Campaign for Nuclear Disarmament and the European Nuclear Disarmament umbrella group are part of a "nonaligned" movement open to all comers that has consistently demanded the removal of Soviet as well as NATO nuclear weapons from the European theater. West German disarmament leaders say much the same thing. At the same time, this does not appear to have filtered down to the large number of protestors who turn out in the streets and focus on Reagan and his spokesmen more than they do on the Soviets or even on their own leaders, who have in most cases agreed to or sought out the missile deployment.

The idea of a Nordic nuclear-free zone has been under strong scrutiny in Scandinavia since 1979 as debates in Norway over prestocking weapons for U.S. Marine reinforcements to use in wartime sparked new concern about war that was intensified by debates over defense spending in Denmark and the NATO missile deployment decision.

Leaders of the then-governing Labor Party in Norway decided to deflect left-wing opposition to the weapons prestocking and Norway's vote for the missile deployment by committing themselves to campaigning internationally for European nuclear disarmament. But when the Norwegians began discussing the proposal with Social Democrats from Denmark, the Netherlands and Belgium, Secretary of State Haig pointedly warned that such a course could undermine NATO unity and interfere with the U.S.-Soviet theater nuclear talks scheduled to begin in Geneva at the end of November.

Brezhnev countered by giving an interview to a Finnish newspaper and declaring that the Soviets were ready to consider talking about making part of the Soviet Union nuclear free if there were a nuclear-free zone "in the north of Europe." But Labor lost the election and was replaced by a Conservative government. When a Soviet submarine apparently carrying nuclear weapons intruded into Sweden earlier this month, Scandinavia diplomats acknowledged that the Nordic nuclear free proposal had been moved to the back of the stove.

"I believe it is impossible to make the proposal for a Nordic nuclear-free zone a positive element in the coming negotiations between the U.S. and the Soviet Union. It is therefore better to let the idea rest," Svenn Stray, Norway's foreign minister, said last week after emerging from a meeting in Washington with Haig.