London — The dust is still settling from three new tactical skirmishes in the battle to sway European opinion for or against NATO's medium-range nuclear deterrent. At stake is whether the United States and Western Europe can retain a united front against a new subtle Soviet strategy.
Involved in the latest maneuvering are:
* The Kremlin, with its latest Warsaw Pact offer to NATO of a nonaggression pact with an apparently fresh readiness to consider on-site verification. This follows earlier offers to reduce medium-range nuclear missiles and to hold a summit meeting with President Reagan.
* The European peace movements, preparing for a year of almost nonstop rallies and meetings to block deployment of NATO cruise and Pershing missiles in Europe. They have welcomed the latest Soviet offer in statements calling on Mr. Reagan to consider it carefully.
* Britain, the closest US ally in Europe, which has just provided NATO and Western Europe with a powerful public advocate against the peace movement and its highly-publicized calls for unilateral European disarmament.
He is the energetic new defense secretary, Michael Heseltine. Sources close to Prime Minister Margaret Thatcher make it clear the main reason he was appointed to replace the retiring John Nott Jan. 6 was that he has the ability to act as a kind of minister of public persuasion.
The sources say that Mr. Heseltine's main job will be to use oratory, which regularly brings Conservative Party conferences to their feet, to argue the case for NATO cruise and Pershing missiles in Europe. Both his appointment - made as NATO capitals were weighing the Warsaw Pact's offer - and the cautious NATO reactions to that offer indicate NATO recognition of the importance of the public persuasion battle.
New Soviet leader Yuri Andropov has encouraged the peace movement and won many headlines with his three recent offers - reduction of medium-range SS-20 missiles, a summit with Mr. Reagan, and now the nonaggression pact.
Here in London, the Campaign for Nuclear Disarmament (CND) immediately issued a statement on the nonaggression pact, echoed by other groups across Europe.
The statement was sympathetic to the USSR, saying the pact offer showed the willingness of the new Soviet leadership ''to engage in genuine disarmament talks.'' CND urged Mr. Reagan and other NATO leaders to consider ''most seriously'' all Soviet offers to date.
CND repeated its call on the Thatcher government here to cancel the introduction of US cruise missiles and the contract to buy US Trident submarine-launched missiles. British and US leaders, CND officials contend, are beginning to realize that they have ''alienated people by rejecting Soviet proposals out of hand.''
CND, together with European Nuclear Disarmament and church, socialist, liberal, environmental, women's, youth and other groups in the Low Countries, West Germany, Italy and elsewhere, plan an entire year of protests in 1983 aimed at blocking the 572 cruise and Pershing missiles intended for deployment by 1984 . The climax, peace officials say, will be a ''hot autumn'' of protest in major capitals.
So far, the Thatcher government reaction to the Warsaw Pact proposal has run along the same lines as the US one - worth study, but not really new. Foreign Secretary Francis Pym has refused to reject the idea outright, but shows a wary recognition that the Warsaw Pact has suggested nonaggres-sion pacts before, and that mere words are not enough.
The official reaction deliberately stops short of an outright rejection since officials here are well aware that Mr. Andropov has been scoring propaganda points with at least some sections of the European public.
Mrs. Thatcher now looks to Mr. Heseltine to bring his drive and public speaking skills to the side of NATO governments. The new defense minister's military experience has been limited to national service in the Welsh Guards in the 1950s. He is a self-made millionaire, highly successful in trade publishing before entering Parliament.
His booming, impassioned rhetoric, and his athletic flamboyance (he once seized the mace on the floor of the House of Commons and flourished it at opposition benches) have earned him the nickname of ''Tarzan'' at Westminster.
He is extremely well-known in Britain for his years as environment minister (which also covers local government). He tried to reduce local government spending (with little success) and worked extremely hard to revive British inner cities, including riot-scarred Liverpool.
As a skillful and effective bureaucratic manager, he will be expected to streamline the massive defense department by looking for economies. But the nature of his appontment is largely political - to take on the peace protestors in public.
He heard of his appointment while bird watching on the island of Tobago, where he claimed to have spotted 70 of the island's 200 species. From now on he will be in the thick of a different kind of fray. He was immediately confronted with a letter from CND urging him, in effect, to support unilateral disarmament.