Deep inside Britain's Ministry of Defense lies what is known by its members as the "Purple Center." Officially, it is the Central Defense Staff, created last January by Defense Secretary Michael Heseltine to bridge the special interests of the three service branches and to provide overall defense policy planning.

One of "Purple's" first jobs has been to coordinate Britain's formal response to the Reagan administration's invitation to participate in its Strategic Defense Initiative, or "Star Wars," research program. For several months, a team headed by chief science adviser Richard Norman has studied SDI documents, supplied its own documents to relevant ministries, been briefed by U.S. officials and briefed British industry representatives.

The result, said an official involved in the process, is "a great uncertainty in our minds" over how Britain will fit into what SDI director Lt. Gen. James Abrahamson has called "a new strategy for the future."

Until that uncertainty is resolved, he said, there can be no official response to the U.S. invitation. Already, the formal acceptance the government hoped could be transmitted before Parliament recesses at the end of July is likely to be delayed until fall.

According to a number of knowledgeable foreign policy and defense officials, Britain's problems are not with the overall concept of research into a space-based missile defense.

Prime Minister Margaret Thatcher, citing ongoing Soviet programs, has backed SDI research in more explicit terms than any other allied leader, in statements after her Camp David meeting with Reagan in December and in her address to Congress in February.

"We've said yes," a senior official repeated last week. ". . . the answer was always going to be yes -- yes, but."

According to this official and others, while the administration has pushed for allied participation in the program, it has been unable to answer what the British government considers key questions about SDI, and the terms under which technical participation in the research phase are being offered.

"We've gone in with simple questions," one official said. "There have been no simple answers."

Among the questions:

How much of the technology researched by British scientists for SDI will be available for use in Britain's own civil and military development programs?

Some of the research "may be helpful in other ways," a foreign policy official noted. "After all, a laser is a laser is a laser."

Will sensitive U.S. technology be available to British scientists collaborating with SDI? Or will the program fall victim to U.S. charges that Europe is the door through which much western technology is leaked to the Soviet Bloc?

"It is of interest to us whether Richard Perle still reigns in the Pentagon," a government scientist said of the assistant defense secretary most identified here with making the accusations. "The last few years, we've found it really difficult to get access to U.S. technology."

Once the relatively small-budget research contracts turn into big-budget "hardware" contracts, jealously guarded by U.S. members of Congress for their own districts, how much will be left for Europe?

"Let's face it," said the scientist, "the really big money on SDI is going to be if and when somebody moves toward hardware. A major doubt in Europe is whether we'll ever get a slice of that action."

These questions and others have been on the table since Defense Secretary Caspar W. Weinberger sent letters to each of the allied governments last March, inviting them to indicate their "interest and areas" of possible contribution to the research program. The letters raised considerable hackles among the allies by giving a deadline of 60 days -- later withdrawn in response to protests -- for individual government responses specifying what they could offer to SDI.

What the Europeans want to know, officials said, is what the administration is selling in return for their participation.

Getting an answer is one part of "Purple's" task. Another is determining the balance between SDI and domestic priorities. There is much talk throughout Europe about whether participation in the $26 billion SDI program would mean a continental "brain drain."

"Virtually all SDI technologies are areas of high interest within our own defense research," an official said. Abrahamson's talk of tapping "the best brains in Europe . . . can be fairly frightening. If you look at some significant areas of SDI, they rest heavily in the area of electronics where worldwide, and certainly in Europe, there is a shortage."

Additionally, allied governments must decide how closely they want to oversee and control the SDI-related activities of their countries' private industry. In Britain, although Thatcher's government opposes interference in the private sector, much of the defense research and development is done by the government and given to private contractors for production.

The government's position is that any company is free to sign an SDI contract. But, officials point out, there is little indication that the Pentagon is ready to sign.

So far, although there are rumors that one French company has obtained an SDI contract, none has been written in Britain. One British researcher, optical physics professor Desmond Smith of Edinburgh's Heriot-Watt University, has been approached by U.S. military officials. But the result has been described as a "gentlemen's agreement" under which Smith will receive a $150,000 grant as soon as Abrahamson is ready to sign contracts.

The British government acknowledges that to refuse participation in SDI is to cut itself off from participating in potential technological advances in a way it cannot afford.

"There are lots of good things in SDI," the foreign policy official said. "I just wish it had been done in a different way."

Following Reagan's initial announcement of the initiative in 1983, he said, "Participation didn't rear its head until last February. Then it became an issue. The Weinberger letter was not quite a bolt from the blue, but it was very much an initiative from the American side" that was "much resented."

For many, including officials in the Thatcher government, the March 26 letter implied a sort of blackmail. Those who signed on in time -- as governments -- might get pieces of the financial and technological pie for themselves and their national industry. Those who did not would be left out.

Officials here said they believed the Weinberger deadline was in large part designed to quickly obtain the higher level of allied political backing for SDI that an official response would imply. This belief was reinforced, they said, by their perception that the administration itself is a long way from being ready to sign any contracts.

The allies argued that 60 days simply was not enough time to make judgments about a program that had been explained in only the vaguest terms at that point.

"It was sign up or be left behind in the revolution," an official said. "That's one of the reasons why the French are out of it, why the Germans are uneasy, and the Japanese have a great deal less enthusiasm than the Pentagon anticipated."

The allies balked, and the deadline was withdrawn. But for the British, the controversy meant added time and leverage to maneuver Washington into a more precise definition of what it was offering.

Officials here agree that the process has advanced somewhat recently, as science adviser Norman has traveled twice to Washington since April. Other officials from both countries have set up a virtual trans-Atlantic shuttle, and technical experts in the British Embassy in Washington are frequent visitors to the SDI office there.

Norman's office has briefed about 20 British companies. "Our job is to know what industry can do," said one participant. "We're briefing them to assist in forming our own opinions. We're encouraging them to formulate proposals."

Abrahamson has made at least three visits to London, where one newspaper described him as "a cherubic Luke Skywalker who positively exudes good intent."

During his most recent visit, two weeks ago, Abrahamson was asked by reporters if it were true that the United States did not really need allied research help for SDI. Couldn't U.S. science really "go it alone?"

Abrahamson paused. "I think we have a capability to do these kinds of things," he said. "But remember, the one thing we can't go alone is we can't provide for the common defense of the West. Our security is inextricably linked together. Therefore, it doesn't make sense to try and go it alone."