Visiting Soviet Politburo member Mikhail Gorbachev issued a clear warning from the Kremlin today that unless the United States agrees to ban weapons in space there is little hope of stopping the nuclear arms race.

The Soviet leadership, including President Konstantin Chernenko, "attaches quite a serious importance" to the "new Soviet-American talks scheduled to start in Geneva with the purpose of reaching mutually acceptable accords on the whole range of issues concerning nuclear and space weapons," Gorbachev said.

But, he added, "I would like to stress that in present circumstances it is especially important to avert the transfer of the arms race to outer space. If it is not done, then it would be unreal to hope to stop the nuclear arms race."

The statement in a luncheon speech was the first public warning since Gorbachev arrived here Saturday of the extraordinary emphasis Moscow is putting on trying to halt Reagan administration projects on space defense, including antisatellite weapons tests and especially the so-called "Star Wars" research effort aimed at nullifying the Soviet offensive missile threat.

His remarks suggest that the Soviet demands on limiting space weaponry could become an immediate problem for the talks on Jan. 7 and 8 in Geneva between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei Gromyko. Those talks are meant to try to work out a formula for resuming arms negotiations suspended since the Soviets walked out at Geneva a year ago.

While the Reagan administration has indicated that it is willing to discuss how to handle space weaponry, Washington has put more emphasis on dealing with the more immediate issue of limiting nuclear-tipped intermediate-range and intercontinental missiles already in place.

Gorbachev's emphasis on space weaponry during his week-long visit to Britain also could be aimed at straining relations between the Reagan administration and the British government of Prime Minister Margaret Thatcher.

Thatcher, in July, called publicly for negotiations and mutual restraint, saying that otherwise "we may see space turned into a new and terrible theater of war." Yesterday, authoritative British sources said that both Britain and the Soviets are concerned about a space arms race and interested in avoiding it.

Some commentators here today said they believed the Soviets will be able to capitalize on this general British concern and thus perhaps try to drive a new wedge between Washington and its allies.

British Foreign Secretary Geoffrey Howe sought to derail any such possibilities today. He cautioned in an interview against "trying to produce any divisions of emphasis there" and said the main point is that all components of the nuclear threat must be reduced, including space.

Until today, Thatcher had not said anything specific about the Star Wars plan. But asked in a BBC interview today about the Soviet demand for a ban, she said: "Obviously you can't stop research from going ahead, but I think one does not want to go into a higher and higher level of armaments."

Because of her views, there is considerable interest here -- and presumably in Moscow -- as to whether Thatcher will express any view to Reagan on the space aspects of the coming Geneva talks when the two meet at Camp David on Dec. 22. Thatcher is the foreign leader closest to Reagan, and Star Wars is the defense program that Reagan appears to feel most strongly about.

British officials said that, in the private talks today between Howe and Gorbachev, almost the entire time was taken up by the space issue and that Gorbachev talked far more about the Star Wars research effort than about the Soviet desire to forestall a scheduled U.S. test in March of an antisatellite system.

Gorbachev's visit, however, continues to be viewed here as positive and a potentially important turning point for British-Soviet relations.

"I like Mr. Gorbachev," Thatcher said in her BBC interview. "We can do business together." She said she was "cautiously optimistic" that the visit would lead to better East-West relations.

"We have two great interests in common," she said: "that we should do everything we can to see war never starts again, so we go into disarmament talks determined to make them succeed; secondly, we think they are more likely to succeed if we can build up confidence and trust in one another and in each other's approach."

In talks with Howe, sources said, Gorbachev stressed the connection between antiballistic missile (ABM) defensive systems and the level of offensive arms. He reportedly used the 1972 U.S.-Soviet agreement limiting ABMs as an example of something that ultimately held down the number of offensive missiles on each side. The implication apparently was that if the United States went ahead with the Star Wars space-based missile defense, it would escalate the offensive arms race as well.

The Reagan administration has emphasized that the Star Wars effort is only a research project and has said that it will be several years before it is known whether the effort is feasible. They also have said the Soviets are working on components that soon could be turned into a less sophisticated ground-based ABM network.

Washington also contends that the Soviets already have a weapon capable of shooting down satellites in low-earth orbit and that the United States thus needs to test a matching capability.