FROM the way British Prime Minister Margaret Thatcher has been working the crowds in the Soviet Union, you might think she was running for office. Well, she probably is, though not, of course, in the Soviet Union. Her five-day visit there, the first by a British prime minister since Harold Wilson's in 1975, was definitely designed with domestic politics in mind. A trip abroad is a great way to enhance the prestige of any political leader - even one like Mrs. Thatcher, already riding high in the polls for some time.
Her trip serves a number of other purposes, though. On one hand, her close ties with President Reagan make her the natural choice as a stand-in, a political alter ego, so to speak, for him in Moscow. She can sound out both the US and the Soviets as progress is made toward an accord on intermediate-range nuclear weapons. And with the Reagan presidency still somewhat in eclipse, the stars of a power like Britain shine a little brighter.
On the other hand, the Moscow visit should also give Mrs. Thatcher additional credibility in the role she has been assuming as spokeswoman for Europe. Already the senior head of government among the Big Seven, she has spent time working toward consensus on defense issues with West Germany and with the other independent nuclear power in Europe, France.
Mrs. Thatcher has also been getting her points in about religious freedom and human rights in the Soviet Union - traveling 40 miles from Moscow to visit a monastery, and scheduling breakfast with a noted refusenik. The Soviets must understand that human rights are something the West as a whole cares deeply about, and are not just an American obsession.
The Soviets are said to be unhappy about the exploitation of the visit for Mrs. Thatcher's own domestic political considerations, but they are hardly in a position to complain. Mr. Gorbachev himself, while still only heir apparent in the Kremlin, got quite a bit of mileage out of the Western publicity machine during his 1984 visit to London. Mrs. Thatcher declared Gorbachev a man she could ``do business with,'' and the West discovered that at least one Kremlin leader has a mediagenic wife who likes to shop while her husband is tied up in meetings.
Labour Party leader Neil Kinnock is also no doubt aware of the value of foreign travel by politicians. He dashed off last week to Washington for a quick visit with President Reagan and secretaries Shultz and Weinberger to explain his ideas for a nonnuclear Britain. Confusion remains about how those ideas were understood in Washington. But in Britain it is clear from polls that those ideas are not being well received. Labour is facing the prospect of being not only No. 2, behind resurgent Tories, but No. 3, behind the Liberal/Social Democratic Alliance.