Thousands of British antinuclear protesters joined hands in Hyde Park today in a human chain that linked the U.S. and Soviet embassies on the 38th anniversary of the first explosion of an atomic bomb.

The event was unusual in that it was directed as much at the Soviet Union as at the United States.

Identical letters were delivered to officials of the two embassies calling on the superpowers to declare an immediate freeze on nuclear weapons.

It was on this date in 1945 that the United States first tested an atomic bomb in the desert near Alamogordo, N.M.

About 6,000 joined the human chain on a sunny afternoon, the hottest in London so far this summer with the temperature in the 90s. A relaxed crowd that ranged from teen-agers sporting rainbow-dyed hair to neatly dressed pensioners gave the affair a cheerful quality. Scores of police and countless tourists looked on.

A large balloon representing the Earth was passed hand-over-hand across the mile and a half that separates the embassies, at opposite ends of the park.

The demonstration was organized by the Campaign for Nuclear Disarmament, the largest of Britain's antinuclear groups. Unlike most protests during the past year, this one was not specifically aimed at the deployment later this year of new U.S. medium-range missiles in Britain.

With deployment now widely accepted as a certainty, unless a Soviet-American agreement on the missiles is reached in the Geneva arms talks, the Campaign for Nuclear Disarmament seems to be emphasizing again its broader opposition to nuclear armament.

"We demand that you agree at once to an immediate freeze on all nuclear weapons," the letters addressed to the Soviet and American embassies said, "as a prelude to making massive unilateral cuts in your nuclear arsenal, leading to multilateral and complete nuclear disarmament."

At the Soviet Union's embassy, where such petitions are less routine than at the United States', an official politely told the group's representatives that the Soviets share the organization's goals.

He said that Moscow had made many proposals calling for arms reduction and a freeze.

Cast in generalities, these proposals have been portrayed by the United States as intended more for show than as a prelude to hard bargaining.

Today's demonstration was the Campaign for Nulcear Disarmament's most ambitious in several months. The biggest of the fall will take place on Oct. 22 when organizers hope to have a huge crowd fill Hyde Park in one last major attempt to influence the Geneva negotiators and the British government before the new medium-range missiles are deployed.

Two weeks ago, the women of the Greenham Common peace camp, located at the gates of the base where the missiles are to be deployed, staged four days of demonstrations in an attempt to blockade the base. Dozens of women were arrested, and the authorities were forced to dispatch substantial contingents of police and military units to keep the protesters under control.

Nonetheless, the demonstrations received relatively little press and public attention here and abroad. The Daily Mirror, which had been sympathic to the Greenham Common women, published an article this week by an undercover reporter who said that the camp had become filthy, that many of the women are lesbians and that few seemed interested any longer in discussing nuclear arms.

Even so, the government still seems to recognize that as deployment of the missiles approaches, a resurgence of the antinuclear movement may well take place. In a meeting with foreign correspondents this week, Defense Minister Michael Heseltine said that there would be no formal ceremony marking the day the missiles become operational. He said that the government had "no intention" of providing its opponents with an opportunity to arouse public sentiment.