British Prime Minister Margaret Thatcher will visit Camp David Saturday for a meeting with President Reagan that British, American and other allied diplomats believe could be crucial in the formulation of long-term U.S. arms control policy, especially involving space weaponry.

The Conservative British leader, fresh from meetings with top-ranking Soviet and Chinese officials, enjoys perhaps more respect and influence and probably the best personal relationship with Reagan of any allied head of government.

But she is faced with a delicate and difficult task in conveying to him her deep concerns that a new arms race in space must be avoided and that the western alliance must not be allowed to be split, either by internal differences or by Moscow, on this controversial issue.

Most at issue is the long-term future of one of Reagan's favorite programs, the $26 billion Strategic Defense Initiative, known as "Star Wars." The project is in the research stage but is aimed ultimately at determining if a futuristic and foolproof space-based system could be developed for defense against missile attack.

Although Thatcher has warned against space being "turned into a new and terrible theater of war," she has refrained from specifically or publicly criticizing the Star Wars project so closely identified with Reagan.

Informed sources here say that Thatcher is not expected to challenge the current U.S. research effort. In an interview this week, she said, "Obviously, you cannot stop research going ahead." She is said to believe that the U.S. effort contains some potentially useful negotiating "leverage" at the bargaining table because Moscow is clearly worried about the U.S. project.

But what Thatcher is concerned about, according to both British and U.S. officials, is the danger and expense that could accompany a space race stimulated by Star Wars that goes beyond research into development and deployment.

Thatcher is said to adhere to the concept of research as embodied in the 1972 U.S.-Soviet agreement limiting antimissile defense systems. This agreement allows research but bans actual development.

Speaking of Star Wars here this week, Thatcher said, "One does not want to go into a higher and higher level of armaments." In an earlier speech, without specifically mentioning Star Wars, she said that if each side "goes on to the next stage of research. . . the other will surely follow" and "within but a short period of time we shall have the same military balance, but at a higher level and a higher cost."

French President Francois Mitterrand publicly indicated disapproval of the Star Wars project this week. West German officials are not enthusiastic and fear its huge costs could sap NATO's conventional strength.

British and foreign diplomats here say there are a lot of potential divisions in the alliance over the project and how it is handled and that it could become what one diplomat called "Son of INF." That is a reference to the splits in the alliance a few years ago over whether to deploy intermediate-range nuclear forces, or missiles, in Western Europe.

The diplomats say the situation could be worse because while the missile deployment plan was controversial, it was an alliance decision and meant to link American and European defense even tighter. The space defense plan, however, is a U.S. plan, and some allies see it as loosening ties to Europe because it would build a defense screen over the United States.

Thatcher, informed sources say, is determined that such divisions be avoided. She is said to be encouraged by reports from Washington that the space projects can be put on the bargaining table if talks next month between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei Gromyko in Geneva lead to resumption of arms control negotiations.

Sources here say Thatcher may say something in support of the U.S. research effort in Washington Saturday to avoid any implication of a U.S.-British split and that she is also determined to emphasize that the just-concluded visit here this week of Soviet Politburo member Mikhail Gorbachev did not put any distance between London and Washington on security issues.

After more than five hours of talks with Gorbachev, who is viewed in the West as Moscow's second in command, an authoritative British source told reporters that both Thatcher and the Russian "expressed a clear interest in avoiding an arms race in space. They are concerned, quite clearly as we are," he said of the Soviets.

Gorbachev made it clear while here that shutting off the U.S. military space efforts was Moscow's top priority. Although Gorbachev pledged that the Soviets would always match new developments, British officials got the impression from the Soviet official that the Kremlin rather not spend the money or may not have it to spend on a new cycle of arms that might leave neither side better off.

The Soviets, according to U.S. intelligence, already have invested heavily in what may be less sophisticated, ground-based components for a future antimissile defense system.