The Carter administration views the new U.S. agreement to sell Trident submarine-launched missiles to Britain as an important boost to the Western alliance and a major effort to restore Britain's dwindling share of atomic firepower within that alliance.

The key to achieving both those goals lies in the vastly more effective atomic punch of the Trident missile over the aging. U.S.-supplied Polaris missiles now in the British submarine fleet.

Although each Polaris missile carries three atomic bombs in its nose, they are fired like buckshot at a single target a maximum of about 2,900 miles away. The new Trident I missiles, however, can carry up to eight individual atomic warheads on each missile and each warhead can be aimed with greater accuracy at different, widely separated, targets, more than 4,000 miles away.

These multiple, independently-targetable warheads are known as MIRVs and both the United States and Soviet Union for the past decade have been rapidly changing over their entire land and submarine-based missile forces to carry these hydraheaded weapons.

The British, however, had not decided to do so until this week.

The 1970, when the British fleet of four Polaris carrying submarines -- each vessel armed with 16 missile -- was becoming operational, Britain accounted for roughly 7 percent of the U.S.-British atomic arsenal aimed at the Soviets. Since then, the British bomber force has all but disappeared and, as the United States has converted to MIRV missiles, the British will be back up to about 7 percent in the 1990s. The British Trident force will also equal about 7 percent of the long-range atomic firepower of the Soviet Union at that time, these officials estimate.

The new U.S.-British agreement was also clearly being seen in Washington as a timely boost to the image of a strengthened alliance at a time when the Carter administration is under sharp attack from Republicans alleging that the White House has let U.S. defenses slide dangerously and weakened relations with U.S. allies.

The letters exchanged by President Carter and British Prime Minister Margaret Thatcher both laid heavy emphasis on mutual pledges to give strong support to a wide range of new projects aimed at beefing up alliance military preparedness.

Thatcher's assurances of Britain's "whole-heartened" support in this matter are expected to become even more important since the Soviet Union, may object to the new agreement as a violation of the noncircumvention provisions of the SALT II pact, which both the United States and Soviet leaders have signed but which has not yet been ratified.

U.S. officials point out, however, that the same provision specifically says that the restriction "will not affect existing patterns of collaboration and cooperation with our allies nor will it preclude cooperation in modernization."

The Soviets may also view the new agreement as an effort by the West to gain insurance against any failure of the alliance to actually go through with a controversial plan to install almost 600 new medium-range U.S.-built Pershing and cruise missiles in Western Europe.

U.S. officials would reject such a Moscow claim, pointing out that the cruise missiles are meant to balance Soviet SS20 missiles already in place while the Tridents are meant to give Britain the ability to maintain its own deterrent force against Soviet attack.

The Soviets, reversing their previous stance, told West German Chancellor Helmut Schmidt last month that they would be willing to discuss negotiations aimed at limiting the new nuclear weapons to be based in Europe.

In Brussels yesterday, U.S. Deputy Secretary of State Warren Christopher told the NATO allies that the United States was ready to start preliminary talks with Moscow on this subject but said it would be a complex and formidable task to prepare for such talks.

Christopher indicated that the next steps in preparing for talks would take place over the next several weeks. "I want to stress that the United States wants to get on with it. We will not be dilatory," he said.

The Soviets want to discuss more than just the new U.S. missiles in these talks. Moscow wants them also to include other so-called "forward bases systems" such as U.S. warplanes based in Europe. But Christopher, according to Reuter, said defining what constituted such systems was apt to be one of the most perplexing issues in the history of arms control.

Another important boost for the U.S.-backed position on negotiating from strength with Moscow also came yesterday when Schmidt said that Western countries should not weaken their resolve to modernize their own weapons because of apparent Soviet readiness for arms limitation talks.

Schmidt, after meeting with Luxembourg's prime minister, told a news conference that both officials were concerned about the hesitancy of some NATO countries.

This seemed to be a pointed reference to Belgium and the Netherlands, which have declined to join Britain, West Germany and Italy in allowing the new U.S. missiles to be stationed on their soil.

Schmidt warned that productive negotiations with Moscow can be expected only if the West leaves no doubt that it is determined to maintain a balance of power with the Soviets.