London — This week's visit to Britain by Mikhail Gorbachev, the No. 2 man in the Kremlin, could provide the West with a clue to Soviet strategy at next month's arms talks in Geneva.
Although nobody here suggests that it represents any grand design put forward by either East or West, the week-long visit by Mr. Gorbachev is part of an interesting conjunction of world leaders.
British Prime Minister Margaret Thatcher, well pleased with a longer-than-anticipated meeting with Gorbachev on Sunday will, within one week, have also met with the top Chinese leadership in Peking before dropping in on President Reagan in the United States on Saturday.
With the impressions of Gorbachev's arms stance still fresh in her mind, Mrs. Thatcher is expected to convey useful information to the President on how Soviet Foreign Minister Andrei Gromyko might play his hand when he meets with his US counterpart, George Shultz, in Geneva on Jan. 7.
British sources stress that since Gorbachev's conversations amount to discussions, not negotiations, precise knowledge of Soviet positions will have to wait until Geneva.
Nevertheless, some of the nuances of Soviet policy are coming through.
Gorbachev, who has won respect for his mastery of detail, has given a lengthy presentation on the Soviet approach to the forthcoming talks.
Much of the speculation about the Soviets' willingness to resume the arms dialogue is predicated on Soviet alarm at President Reagan's strategy for a ''star wars'' defense against incoming nuclear missiles.
The Americans are pushing ahead with testing new space weaponry more advanced than the Soviets currently possess. Hence, Moscow is expected to push for a US moratorium on the testing of advanced antisatellite weapons early next year.
Gorbachev has indicated that as far as the Soviets are concerned, all types of nuclear weapons, including weapons in space, should be discussed at the Geneva talks.
With Gorbachev discussions with both Prime Minister Thatcher and the foreign secretary, Sir Geoffrey Howe, going as well as they did, some diplomats here are trying to dampen down expectations that next month's talks could produce a breakthrough in the arms stalemate.
A more realistic view, they say, is that negotiations are likely to be part of a slow, patient, ongoing process that would in turn lead to more talks.
Gorbachev's delegation has not yet tipped its hand as to when or where the Soviets would like substantive talks to begin.
Yet hopes for arms talks have been raised precisely because Soviet responses are now more forthcoming - as reflected in Gorbachev's visit here this week, in Mr. Gromyko's forthcoming trips to Geneva and Rome, and in Soviet President Konstantin Chernenko's proposed March meeting with French President Francois Mitterrand in Paris.
As one well-informed source put it, the Soviets are no longer ''sulking in their tents,'' as they were a year ago when they walked out of arms talks in protest of European deployment of US cruise and Pershing II missiles.
Thus Gorbachev's warm and friendly tone, while not in any way minimizing deep East-West differences, is greeted as possibly heralding a much-needed improvement in East-West relations.
Although the official Soviet press alluded to ''frank'' discussions in Britain - meaning sharp differences - Moscow has reacted positively to the British talks.
Soviet television gave the visit a solid five-minute coverage. Gorbachev himself expressed the hope that if Anglo-Soviet relations could be improved, the effect might spread.
Although the Soviet Union has recently announced a substantial boost in military arms budget, there is an apparent readiness to back down if the US makes reciprocal cuts in military spending.
In his September address to the United Nations General Assembly, President Reagan spoke of the possibility of mutual budget reductions.
Gorbachev had already indicated in a recent meeting with visiting US trade officials that Moscow was ready for such reciprocal cuts.
On his arrival here, Gorbachev hammered home the message equally forcibly: ''There are no types of armament that the USSR would not agree to see limited and eventually banned, in agreement with other states on a reciprocal basis.''
Gorbachev said that he was looking forward to a ''frank exchange of opinion'' in Britain on ways to overcome ''the present dangerous development of the international situation and make things in the world healthier again.''
Such remarks so early on in Gorbachev's visit and the amount of time he is spending here - he arrived last Saturday and leaves this Saturday after extensive traveling around Britain - is taken as a measure of the importance the Soviets' second-in-command attaches to his British visit.
Gorbachev realizes that on arms talks and a number of critical foreign issues , Mrs. Thatcher is President Reagan's closest ally.
At the same time, the British prime minister shares Soviet misgivings about ''star wars'' weaponry, but for different reasons. The British maintain it is too costly and dangerous. Besides, a star-wars defense would wreak havoc with the Trident program, Britain's controversial nuclear deterrent.
For the British, the interest in the Gorbachev visit goes beyond next month's arms talks.
As the supposed heir apparent to the Russian leadership, Gorbachev heads the ''most important delegation from the Soviet Union to Britain for many a year,'' according to the speaker of the House of Commons, Bernard Weatherill. Mr. Weatherill was welcoming Gorbachev in his capacity as honorary vice-president of the British group of the Inter-Parliamentary Union, which organized the trip.
For Sovietologists the week-long visit provides a rare opportunity to observe at close quarters the Kremlin's rising star. His good humor, urbanity, and businesslike approach have confirmed earlier impressions of the Soviet Union's No. 2 official as a charming, but formidable, negotiator.
Because of his relative youth and energetic past record, particularly in the area of agriculture and management, much is made of his ''progressive'' credentials.
Kremlinologists warn that while Gorbachev has been depicted as a progressive, that does not make him a liberal.
British sources have been quick to note that in substance Gorbachev has not offered anything novel or unorthodox. Where he is different from other Soviet leaders is in his style and presentation.
When pressed to a definition, a British source said ''very relaxed, and not without humor.''