About 250,000 people demonstrated here today in Britain's biggest march and rally against nuclear weapons, reflecting the recent strong resurgence of the nuclear disarmament movement.

The all-day demonstration, the first of several planned in Western European capitals to mark U.N. Disarmament Week, was similar in size to a large West German nuclear disarmament rally two weeks ago in Bonn. It also was by far the biggest staged by Britain's Campaign for Nuclear Disarmament since 1960, when 100,000 Britons joined in a ban-the-bomb march.

In Rome 200,000 people, shaking their fists and chanting "Reagan is a hangman," marched past the heavily guarded American Embassy, in the Italian capital's largest demonstration in a decade, The Associated Press reported.

Marchers carried coffins and cardboard models of missiles. Some dressed up as skeletons and beat drums. More than 400 buses and 12 special trains brought demonstrators from outside of Rome. Antinuclear demonstrations are planned for Sunday in Brussels and Paris.

It took five hours on a cool, overcast autumn day for all the British demonstrators to march the mile from staging areas along the Thames River through central London to the rally near Speakers' Corner in Hyde Park. The swelling crowd was urged in speeches, songs and poems to do everything possible to ban American and British nuclear weapons from this country and advance disarmament in the West and East.

"This is one of the greatest days in the history of this democracy," opposition Labor Party leader Michael Foot told the crowd. "The size of this demonstration shows that we are not prepared to give in to the dictates of the arms race."

Foot, other speakers and many marchers attributed today's large turnout and other signs of considerable growth in nuclear disarmament sentiment during the past year here to growing fears that the United States and the Soviet Union might fight a limited nuclear war in Europe, sparing their own homelands.

They said these fears were heightened when President Reagan said a week ago that he could envision the exchange of tactical nuclear weapons on a European battlefield "without it bringing either one of the major powers to pushing the button."

"No American president should talk in such terms," said Foot, a veteran disarmament campaigner whose party's policy is to ban all nuclear weapons and American bases from Britain if it regains power.

"I can't dismiss Reagan's remarks as a gaffe," Foot told reporters at today's rally, "because the Western alliance strategy is based on a so-called flexible response adopted by NATO in 1967 in which in some circumstances the West could strike first" with battlefield nuclear weapons.

He and other speakers said the disarmament movement's first priority was to try to stop deployment of American cruise missiles in Britain beginning in late 1983 as part of the NATO alliance's modernization of theater nuclear weapons. Foot said Britain should press the Reagan administration to pursue the "zero option" of foregoing all deployment of the cruise missiles and Pershing II missiles in five NATO countries in the European theater nuclear force negotiations with the Soviet Union scheduled to begin in Geneva Nov. 30.

Earlier this week NATO's defense ministers meeting in Scotland as the Nuclear Planning Group formally recognized that option -- with U.S. objection -- in a declaration. Under the option the West would forego stationing the 572 new missiles in Western Europe if the Soviet Union would dismantle its SS20 nuclear missiles targeted on Western Europe. However, experts believe the option is not very practical as the Soviet Union is highly unlikely to dismantle its SS20 missiles, and the United States in any case would probably also demand the Soviets remove other tactical nuclear weapons as well.

The Pershing and cruise missiles are to replace some of the thousands of aging nuclear warheads the United States has had deployed in Europe for two decades.

Because Europe has no seat at those talks, historian E.P. Thompson, the intellectual leader of Britain's nuclear disarmament movement, told the crowd, "We must take to the streets. Our movement is the third party in the negotiations."

Assistant Secretary of State for European Affairs Lawrence Eagleburger, in Paris for a private conference on disarmament, issued a statement saying the arguments of the antinuclear weapons movement are "precisely that form of thought that the Soviets seek to stimulate by a concerted offensive of propaganda and disinformation," United Press International reported.

Many of the signs carried by demonstrators and some of what they told reporters conveyed more anti-American sentiment than has previously been expressed here. "Europe is not Reagan's to Sacrifice," "Yanks Go Home," "We Are Not America's Guinea Pigs," and "U.S. -- Traitors to the Human Race" were among some of the placard slogans.

"President Reagan is a very good recruiting sergeant for this movement," said one marcher, 39-year-old Tony Simpson of Bristol. "All this saber-rattling he does is getting a lot of European people worried and afraid of getting nuclear war in Europe without the United States being involved."

"America has to be told that it's Europe's business to decide how to defend itself," London statistician Ian Plewis told a reporter. "We need some kind of strictly European defense."

"President Reagan does not own Britain and Europe," former Labor Cabinet member Tony Benn declared to the cheering throng. Benn is a leading advocate of removing all of the several dozen American military installations in Britain.

Thompson, however, urged that the Western European nuclear disarmament movement also pressure the Soviets to reduce or eliminate the SS20 missiles. "We ask the Soviet television and press who are present at this meeting to report our demands fully to the Soviet people," Thompson said. "Don't tell them there was a great meeting in London protesting NATO's plans. That's only half the truth. Tell them there was a meeting to get nuclear weapons out of the whole continent, including the SS20s."

Today's turnout appeared to confirm claims by the Campaign for Nuclear Disarmament, founded in 1958, that its national paid membership has jumped from 3,000 to 32,000 in the past 18 months. According to its general secretary, Msgr. Bruce Kent, there also are now 1,000 local disarmament groups with up to 1,000 members each scattered around Britain.

Banners denoting many of those groups from England, Scotland and Wales could be seen in the crowd today, along with the official insignias of dozens of labor union locals. Both Britain's Trades Union Congress and the union-based Labor Party overwhelmingly adopted strong resolutions at their national conferences this year calling for nuclear weapons and American bases to be banned from Britain.

Annette Parker, 32, from Cornwall in southwestern England, said the disarmament movement in Britain appeared now to be much more broadly based than during the past ten years she has marched in demonstrations. "It's not just your freaks anymore," she said. "There's a lot of straight people here who have decided to stand up and be counted. And this is one way to do it."