The United States is very close to signing agreements with the British and West German governments that would pave the way for European companies to participate in research on the administration's Strategic Defense Initiative, according to Defense Department and European diplomatic sources.

The two agreements represent a major breakthrough for the Reagan administration's campaign to gain allied backing for its controversial plans to try to develop a space-based system for defense against nuclear missiles, popularly known as "Stars Wars" here and in Western Europe. The accords would also represent a setback for the Soviet Union, which has campaigned strenuously against European support for the U.S. research project.

U.S. defense industry sources believe that the administration is eager for European participation in order to claim the controversial project as an important part of U.S.-NATO relations. That would make it harder for SDI opponents to derail the program, the industry sources added.

Congress has been reluctant to approve all of the Reagan administration's plans for SDI research. The conference report on a defense authorization bill, pending in the House, would provide $2.75 billion of the $3.7 billion requested by the administration.

The proposed agreements are the first fruits of an intensive SDI sales effort led by Lt. Gen. James A. Abrahamson, chief of the strategic defense agency, who has held talks with eight foreign governments and traveled to Europe "four or five times" in the past six months, according to an aide.

A senior West German official, during a recent visit to the United States, said Bonn's backing for SDI could be "decisive" in persuading other NATO allies to follow suit and in undermining Soviet attempts to discredit the project.

It is unclear when the first agreements will be signed, but a Pentagon official predicted "it should all happen during the fall." The British and West Germans are now involved in intense negotiations with the Pentagon on details of an agreement that may take the form of a "memorandum of understanding."

Not all U.S. allies have responded as favorably as the British and West Germans. France, Denmark, Norway and Canada have formally refused to play any role, and Japan has shown reluctance, but Italy has signaled definite interest.

Despite the tepid response from some allies, Pentagon officials are quick to emphasize that foreign contractors can nevertheless participate without an overarching agreement between governments that is intended to resolve many of the technical details, such as access to top-secret data. French and Canadian companies are being encouraged by SDI officials to join the effort even without official sanction from their governments.

A 28-member West German delegation, led by national security adviser Horst Teltschik, last Friday completed a 10-day tour that included visits to research laboratories and defense contractors throughout the United States.

"They came with 218 questions altogether and they got the answers on all the subjects included in the list," a West German official said. "They have a good basis for a decision to be taken."

In Bonn, government officials said West German participation in SDI research was now likely following assurances from the Reagan administration that German firms would be able to exploit the technological spinoffs from their involvement, Washington Post correspondent William Drozdiak reported yesterday.

The West Germans are particularly eager to retain some influence over future developments in the antimissile defense system, as well as its impact on arms control negotiations, Drozdiak reported.

By displaying loyalty to President Reagan in endorsing SDI research, Chancellor Helmut Kohl would "feel more comfortable" in urging U.S. limits on SDI testing and development. Kohl, who is scheduled to see Reagan here next month, could also use his role as a moderator to seek Soviet cooperation in cutting superpower missile forces, especially the intermediate-range Soviet missiles threatening Western Europe, the Bonn officials added.

A member of the West German delegation here stressed that Bonn's involvement will be limited to research. Any U.S. decision on either testing or deploying a new defensive system is not expected for years. However, the Pentagon would like to begin testing prototypes of potential SDI components in the near future.

European press reports indicate that the British and West German governments have been pressured by their respective defense contractors to accelerate negotiations with Washington on topics ranging from patent rights to technology sharing to access to top-secret information.

The British government reportedly asked increasingly impatient British firms in August to delay signing any contracts until the government-to-government agreement was completed.

A team of Pentagon lawyers visited London earlier this month to hammer out final details of a bilateral accord. A source close to these negotiations said the question for the British was no longer "whether to participate" but the "procedures and modalities" of this involvement.

"There is a lot of political will in London and Washington to have Britain the first to sign," he said.

Among the still-unresolved questions for the British government, according to this source, is "some kind of U.S. commitment" that British firms will be given a "substantial and significant" share of the research contracts.

Reports in London said that British Defense Minister Michael Heseltine, during talks here July 22 with Defense Secretary Caspar W. Weinberger, asked for a U.S. pledge of at least $1.5 billion in contracts for British firms.

Pentagon officials refused to comment on these reports. The source close to the U.S.-British negotiations noted that figures varying from $1 billion to $2 billion had appeared in the British press but said there was "no magic number" so long as it was "a serious, substantial thing."

Pentagon officials deny that Abrahamson has deliberately used the lure of lucrative contracts to "stampede" nervous or internally divided European governments into participating. But it is clear that the Pentagon is delighted with the positive response from many European private firms.

"There are many, many European companies that have expressed great interest in the program," remarked one SDI official.

Among the French firms showing strong interest is the state-controlled defense consortium Matra, whose chairman, Jean-Luc Lagardere, issued a statement in June favoring participation and proposing that interested European companies form a "club" to discuss the issue with the Pentagon.

Matra, which does research on optic microelectronics and software, is reported to have gone ahead and cultivated its own contacts with the SDI organization here, as have several major West German defense concerns.