The governing body of the Church of England, led by the archbishop of Canterbury, today defeated by 338 to 100 a resolution that would have supported the unilateral nuclear disarmament of Britain.

The church synod of bishops, priests and lay people, went on to approve, 275-222, a resolution endorsing multilateral nuclear disarmament and rejecting first use of the weapons.

With television transmitting the 4 1/2-hour debate nationally, the nuclear issue transformed the normally arcane synod into a focus of British attention. The outcome was seen as a setback for the growing Campaign for Nuclear Disarmament, which is planning major demonstrations this spring and summer against the planned installation of cruise missiles in Britain, and a victory for Prime Minister Margaret Thatcher's Conservative government.

As the synod debate began, Vice President Bush left Britain at the end of a European tour that was designed to win support for the NATO plan to install cruise and Pershing II intermediate-range missiles in Western Europe. Britain is to start receiving the 160 cruise later this year.

An official of the U.S. Embassy sat in the audience during the synod debate at Church House, near Westminster Abbey.

The archbishop of Canterbury, the Rt. Rev. Robert Runcie, launched a frontal attack on the proposal for British unilateral nuclear disarmament and the suggestion that this would improve the chances of disarmament talks in Geneva.

"Is there not a moral inconsistency in seeking to remain within an alliance which accepts a policy of nuclear deterrence while declining to take one's share in the means by which that policy is sustained?" he asked. "I do not believe that unilateral measures . . . will in fact have the effect of 'getting multilateral reductions moving'."

Runcie said he supported Pope John Paul II's view that deterrence based on balance was morally acceptable as a step on the way to progressive disarmament. But he voiced the fears and the powerlessness of many moral philosophers when he observed that "it may be possible to enter a just war in which gains will be proportionable to inevitable damage, but there can be no such thing as just mutual obliteration."

Although Runcie won Britain's Military Cross for bravery in World War II, he does not have a reputation for being sympathetic to military viewpoints. His sermon last year at a memorial service in St. Paul's Cathedral for the Falklands War dead was a low-keyed lament about the evil of warfare. It angered Thatcher and her Cabinet, who had expected a more positive approach to Britain's success.

Also rejecting unilateral nuclear disarmament, Bishop of London Graham Leonard declared that churchmen could not talk about ways of maintaining justice, freedom and peace "if renunciation is the only morally acceptable way and deterrence is ruled out."

But the bishop of Salisbury, the Rt. Rev. John Baker, who headed a committee that proposed the unilateral nuclear disarmament motion, won loud applause when he defended his plan: to scrap Britain's Polaris missile-carrying submarines, cancel plans to buy U.S. Trident submarines and end British manufacture of nuclear weapons.

The Church of England, nominally headed by the queen, is the most prominent member of the worldwide Anglican communion that includes the Episcopal Church in the United States. The Anglican Church has about 65 million followers and the archbishop of Canterbury plays a leading role in it, although each national church is autonomous.

In the United States, the Roman Catholic Church has taken a major role in questioning nuclear policy. A pastoral letter drafted by a committee of bishops condemns even a threat to use nuclear weapons and is expected to be adopted after modification.

The 550-member synod's position in favor of multilateral disarmament is expected to have a significant impact among adherents but is not likely to alter the campaign of those pressing unilateral disarmament--such as a band of women who have been demonstrating outside the Greenham Common U.S. airbase where the cruises are to be installed.

Support for the Anglican Church, which has deep roots in Britain's middle class, has been declining for many years. The sense of frustration of the church's elder statesmen in dealing with a moral issue that seems beyond solution was spelled out by the archbishop of York, the Rt. Rev. Stuart Blanch, who ranks second after the archbishop of Canterbury.

"This debate is about the end of the world and how we can prevent it, or at best delay it," he said. "There is no system of surveillance which can eventually prevent the manufacture of nuclear weapons. While we have to do everything in our power to reduce the likelihood of nuclear disaster, we cannot again ever exclude it. From now on, every generation will be aware that it could be the last generation on earth."