Britain today became the first country to sign a formal agreement to participate in the research phase of the Reagan administration's Strategic Defense Initiative.

A 12-page memorandum of understanding, outlining a framework for British scientists and industry to take part in the controversial, multibillion-dollar program, was initialed at a news conference by U.S. Defense Secretary Caspar W. Weinberger and his British counterpart, Michael Heseltine. The Reagan administration expects the agreement to be a major asset in helping to persuade Congress to fund the program fully by demonstrating that it is supported by U.S. allies.

In addition, Weinberger and other U.S. officials hailed the accord as proof that what they described as a Soviet propaganda campaign to divide the Atlantic Alliance over SDI is not working.

Weinberger said he now anticipated early agreement with "two or three" other countries, although he declined to name them. West Germany and Italy are believed to have been waiting to see what kind of deal the British would forge.

The memorandum signed today was not made public, but both British and U.S. officials said it contained no figures guaranteeing Britain a specific portion of the $26 billion the administration has said will be needed to fund the first five years of the SDI program.

Nor does the accord set out specific assurances, requested by Britain, that it will have access to and ownership of all technology developed here under SDI contract.

But the officials said it "lays down the ground rules" for British participation and provides a "political commitment" that Britain will play "a significant role" in the program.

Heseltine described "substantial opportunities for British companies to win contracts that will bring significant numbers of jobs to this country" and help Britain maintain a technological edge in defense fields.

The agreement outlines at least 18 areas, including laser, computer and optics research, in which British scientists and defense firms have special expertise applicable to SDI. In addition, it establishes a "Strategic Defense Office" within the Defense Ministry here to facilitate and coordinate the matching of SDI contracts with British bids.

Weinberger said it would quickly bring "substantial awards" of SDI-related contracts here. Other U.S. officials said they expected at least two relatively small contracts to be signed almost "immediately."

Since Reagan announced the SDI, or "Star Wars," program in the spring of 1983, British Prime Minister Margaret Thatcher has been its most public supporter among the NATO allies. But Thatcher has had numerous reservations about SDI, and her government used the promise of official support for British participation as leverage to force the administration to address them.

Today's accord follows nearly six months of tough negotiations and sometimes heated disagreements. Although a senior British official acknowledged that Britain did not achieve all of its goals, he said his government was "absolutely satisfied" that it had "pushed the administration as far as it would go."

Britain's concerns were threefold. From the start, while Thatcher agreed with Reagan that the West must match existing Soviet research into a space missile defense system, she was concerned that the SDI program could undercut nuclear deterrence strategy and violate the Antiballistic Missile Treaty limiting U.S. and Soviet development of defensive systems.

Thatcher first addressed that question in a Camp David meeting with Reagan in December 1983, pressing the U.S. administration into a joint communique committing it to policies that would "enhance" deterrence, and an agreement that any SDI advancement beyond research into development or deployment would, "in view of treaty obligations, have to be a matter for negotiations."

British officials repeatedly have made clear that they view the latter point as a U.S. assurance that it shares a "restrictive" interpretation of the ABM treaty. Officials here have expressed frequent concern over statements by some administration officials that Reagan subscribes to a looser ABM interpretation that would allow SDI development and deployment.

Although there was no indication that today's accord was conditioned on a newly specific administration reaffirmation of the restrictive ABM reading, sources said that the memorandum of understanding contains a reference to the 1983 Reagan-Thatcher communique.

Asked whether today's accord should be seen as Britain's "strategic and political endorsement of SDI," Heseltine answered with a pointed reference to the Camp David communique as expressing the "joint views" of both governments.

Britain's other two concerns revolved around what officials here called the "commercial side" of SDI. Thatcher's political opponents and many in the defense industry had accused her government of failing to drive hard bargains in previous cooperation agreements with the United States. In the past, they argued, most of the jobs and much of the ownership of British technology developed under U.S. contract had ended up in the United States.

By promising British researchers and defense firms that it could obtain better terms governing all SDI contracts through a government-to-government agreement, Thatcher persuaded local industry to refrain from signing up on its own. Until satisfactory agreement was reached on its behalf, industry here was promised, Britain would withhold the blanket political approval of the program that the Reagan administration sought.

Last July, Heseltine told Weinberger, in what by most accounts was a sharply worded session, that Britain expected at least $1.5 billion in U.S. contracts and free use of any SDI-based technology developed here. The U.S. administration's refusal, based on insistence that government contract and security regulations barred such guarantees, led to an impasse that lasted until a Weinberger-Heseltine meeting a month ago in Brussels.

The result was today's agreement. While it appears to favor the U.S. negotiating position, one U.S. official acknowledged that "they certainly stretched our limits as far as they would go. They got the best deal we were willing to give."

In addition to recognizing the 18 areas in which British expertise is recognized and sought, the accord refers to several existing bilateral agreements on defense and intelligence exchanges that both governments hope can be expanded to cover some of Britain's concerns on the transfer of SDI technology.

The agreement, Weinberger said, is not designed to "give any special advantages," but rather "provides for the fullest possible participation with the fullest possible retention of the benefits of that participation."

Officials said that a second, more specific agreement currently is being negotiated in Washington to serve as an appendix to the accord signed here today.

"At the moment the signs are auspicious" that the United States sincerely intends to give Britain much of what it wants, a British official said. But, he said, "check back again in six months," after the first contracts have been signed.

"The proof of this pudding," he said, "is definitely going to be in the eating."