BRITISH PRIME MINISTERS frequently perform the useful service of conveying European anxieties to American presidents. That's what Margaret Thatcher was doing this week in Washington. Because she agrees with Mr. Reagan's view of the world, and is a conservative in his sense of the word, she can undertake that delicate duty with less risk of misunderstanding than other Western European politicians might. In her address to Congress she reminded her audience that Europeans consider themselves active contributors to the alliance, entitled to a voice in the great questions of Western policy.

Regarding the Strategic Defense Initiative, Mr. Reagan's project to build a defense against nuclear missiles, she underlined an important distinction. She firmly supports the president's decision to pursue the scientific research that the concept requires, she told Congress. But deployment is another matter. The United States and the Soviet Union have signed a treaty limiting anti-ballistic missile systems. If research now leads toward deployment, she said, "that would of course be a matter for negotiation under the treaty." Those words "of course" were a tactful touch. In fact, there are people here in Washington who talk as though the treaty were almost a dead letter. In urging Americans to keep any new developments within the bounds of negotiated arms control agreements, she was reflecting a view deeply held in Europe.

With similar tact, Mrs. Thatcher cast the economic issues in terms of the industrial countries' obligations to the Third World. She was too restrained (and too skillful) to make any references to subjects of such local sensitivity as budget deficits and trade balances. But she observed that the ways in which "we in the developed countries" manage economic policy affects growth rates and the availability of capital for everyone else. Europeans are sharply aware that their own prosperity depends on the American expansion and what happens next to the American dollar.

Europeans see the American economy sliding farther and farther out of balance under a government that keeps congratulating itself on its economic successes. The Europeans worry about an America that seems prepared simply to ignore the growing extent to which its good life depends on money borrowed from the rest of the world. Amid the pleasantries and compliments she said: "We cannot preach economic adjustment to them" -- the poor countries -- "and refuse to practice it at home." That line should have made her audience, both at the Capitol and at the White House, at least a little uncomfortable.