Defying a drenching downpour, they marched out of the past and through the streets of central London last weekend, chanting "ban the bomb" and carrying signs declaring "no cruise missiles here," "no successor to Polaris" and "nuclear weapons no, peace yes."

In Hyde Park, between claps of thunder, they heard speaker after speaker from the left-wing of the opposition Labor Party, which sponsored the demonstration, call for unilateral disarmament by Britain. They urged that deployment of new U.S. cruise nuclear missiles at NATO bases here be stopped, that other NATO nuclear weapons be removed from British soil, and that Britain's own Polaris nuclear missiles be scrapped.

Nearly 20,000 people from all over Britian turned out for the largest anti-nuclear arms demonstration in Britain since the ban-the-bomb marches of the 1950s and 1960s and the first peace rally sponsored by a major political party since Suez in 1956. The Labor Party's deputy leader, Michael Foot, called it "the beginning of a new campaign in which we can give the lead to the people of Europe and the world." c

Although still small by comparison to the peace marches of the past, yesterday's rally was the latest sign of growing public worry here about nuclear war in the wake of the Soviet invasion of Afghanistan, the debate among the allies over upgrading NATO's nuclear arsenal in Europe and the several false nuclear alerts caused by a faulty U.S. military computer system.

An upsurge of public concern about civil defense, spurred by newspaper and television examinations of Britain's meager, outmoded means for coping with a nuclear attack, has prompted a major government inquiry into possible improvements. Manufacturers of backyard fallout shelters costing $2,000 to $20,000 and up have been inundated with orders.

The long dormant nuclear disarmament lobby here is regrouping. The Committee for Nuclear Disarmament, nucleus of the old ban-the-bomb movement, claims that membership applications have doubled in the past six months. New local antinuclear weapons groups have sprung up and held demonstrations this spring in the cities of Manchester and Leeds and at several British bases.

Over the objections of its leaders former prime minister James Callaghan, the Labor Party has officially opposed the decision by Prime Minister Margaret Thatcher's Conservative government to allow U.S. ground-launched cruise missiles to be based here beginning in 1983. It also opposes replacing Britain's independent nuclear deterrent after the present submarine-launched Polaris missile system becomes obsolete during the 1990s. And the party's ascendant left wing wants Britain to ban all nuclear weapons unilaterally and withdraw from NATO.

Britian last week became the first ally to designate bases where the self-propelled cruise missiles would be kept on a flatbed trucks that could be moved around the country to conceal their locations. Moscow Radio reacted immediately by warning that this decision could become "a deadly boomerang" for the British in the event of nuclear war.

The allies decided last December to upgrade NATO's nuclear arsenal in Europe with 464 cruise missiles and 108 Pershing II rockets based in Britain, West Germany, Italy, Belgium and Holland and targeted on the Soviet Union. But Belgium and Holland have put off final decisions on accepting the weapons on their soil, and West Germany and Italy are moving slowly in searching for sites.

Britian is expected to stand by its decision and remain the alliance's most dependable European nuclear weapon base, despite the resurgence of minority political and popular opposition. But there is much wider and more high-level skepticism about whether Britain also needs and can afford to maintain its own independent nuclear deterrent.

Although a final decision still has not been made, Thatcher and her defense officials still strongly favor replacing Britain's aging Polaris submarines with American Trident submarine-launched missiles and with British-made nuclear warheads. This would cost an estimated $12 billion or more, which alarms Thatcher's own treasury officials.

Some of her Cabinet ministers fear that further big increases in deffense spending cannot be supported by the country's sagging economy or politically justified when big cuts are being made in basic welfare state social programs. Some respected defense experts outside the government have warned that paying for Trident could force major cuts in spending on Britain's conventional military forces and even reductions in its contributions to NATO land forces in West Germany or the naval defense of Europe.

The alternatives of cheaper cruise missiles made by Britain or the abandonment of an independent British nuclear deterrent have been suggested in a debate occurring mostly in the British press. This is because the government has hidden its deliberations over the successor to Polaris behind a thick curtain of secrecy. The debate revolves around the question of how vital it is for Britain to keep its own finger on the nuclear trigger.

One of the points being made by leaders of the new disarmament movement, such as Sussix University lecturer Mary Kaldor, is that the United States and NATO already control most of the nuclear weapons based here.

A routine review by Thatcher's government and examinations by the media revealed that the country had virtually no shelter or evacuation program and was spending less and less money on civil defense every year.

When one television documentary showed that Switzerland is providing a home or public bomb shelter for every one of its citizens, British viewers swamped the Swiss Embassy with questions. The answers -- plenty of money and mountains -- may not be much help here.

The financially hard-pressed Thatcher government was not planning on increasing civil defense spending at all before Parliament insisted that it think again. This task was given to a promising young Cabinet minister, Leon Brittain, who said he has been impressed by the "real public concern" evidenced in the stacks of mail he has received and "the people who come up to me on the street to talk about civil defense. People are now thinking about the possibility of nuclear war who had not been before."

Brittain's problem is to find ways to improve civil defense preparedness without spending much more money. The first steps will be to promulgate government guidelines for the private purchase of backyard shelters, replenish government stocks of emergency food and equipment and put flesh back on the skelton of the nationwide volunteer civil defense network left from World War II.

But Brittain warned that the government cannot assure a bomb shelter for every Briton.

"To give everyone a shelter would be prohibitively expensive," he said. "We don't want to build up the expectation that this is going to happen."

Meanwhile, private shelter suppliers are multiplying rapidly and offering a variety of concrete, fiberglass and plastic containers that can be buried in a homeowner's backyard.

"People are scared, said one shelter maker, George Eliott. "i have to calm them down. They want their shelters right now."