"Come on in" will be British Prime Minister Margaret Thatcher's siren song this week to an American public already shivering from the first chill blast of a Reagan administration economic master plan that is at least first cousin to her own. The water is, uh, fine.

Bracing might be a better word. After almost two years of the Thatcher government's radical, monetarist economic theory, The Times (of London) reports that British manufacturing is in the throes of "one of the worst slumps . . . in this century," with no sign of recovery in sight. While production slides off, unemployment soars into double digits: up to 15 percent in the North, 30 percent or more in some industrial centers.

"The recession in British industry is getting worse," The Times grimly warns.

But never mind. The inflation rate is getting better, plummeting from a high of 23 percent last year to something like 15 percent today. While the worst of the economic stagnation is yet to come, a case can be made that the battle of Britain against inflation is slowly being won -- that the Thatcher/Reagan economic theories work.

And that is the case that Thatcher will cheerfully, confidently make to the president, to Aemrican business groups and to the public at large in the course of her visit to Washington this week.

"The jury is still out" on Thatcherism, as one knowledgeable American official puts it. But this is not likely to get in the way of what promises to be one of the great love feasts in the long history of what will be loosely referred to more than once this week as the Anglo-American "special relationship."

I say "loosely" only because this supposedly "special relationship" is not so much a tradition as it is a sometime thing, evoked for particular purposes at particularly propitious times. One thinks of the pen-pal relationship between Winston Churchill and Franklin Roosevelt; one forgets Suez, or John F. Kennedy being taken neatly to the cleaners in the matter of the Skybolt missile at Nassau by his good friend Harold Macmillan, or Lyndon Johnson upbraiding the British over their sale of buses to Cuba.

Right now, however, is one of those times when you'd have to say that "special" fits. It is hard to remember when a president of the United States and a British prime minister have been so remarkably of one mind, not just on their economic theories but on their fundamental world view.

And it is hard to imagine a more useful opportunity for Reagan and Thatcher to meet. Reagan needs not only Thatcher's reinforcement for his economic designs but her evident enthusiasm for the Reagan tough line on the global Soviet threat. Thatcher can only profit from Reagan's endorsement of her profoundly unpopular economic policies.

Beyond that, if she is not alone, she stands at least apart from allied leaders in Europe (most notably the Germans and the French) in her distrust of detente and her hard-nosed assessment of the Soviet challenge. Her Tory party chafes under the "Little England" role. With her will be her activist, avuncular foreign minister, Lord Carrington. he has high hopes and quite specific plans for a leading British role in a developing new European "initiative" to break the deadlock in the Arab-Israeli conflict.

Lord Carrington, who managed to turn his own boss around on the British approach to Zimbabwe, with striking success, may try to shake Ronald Reagan loose from established policies on Palestine -- including specifically the American refusal to have dealings with the PLO.

Another agenda item is the revitalization and revamping of the North Atlantic Treaty Organization, with the United States and Britain working, the hope would be, hand in hand.

On such matters, however, "exploration" is all that's expected: The Reagan administration is still settling in. So even where large potential differences exist, all the "noises" (as one American diplomat puts it) will be "ecstatic on both sides. What will come through is an extraordinary coincidence of view, a real psychological affinity."

How long can it last? The United States, after all, has interests of its own, with the rest of the allies, with Israel, with the Persian Gulf, with Central America. In all matters, the interests of the United States and Britain cannot be expected to coincide.

But let's not be churlish. It is nice to know that for now the president of the United States and the prime minister of Great Britain, on very basic questions of economics and geopolitics, are to a remarkable degree on the same track. We'll know soon enough whether they will stay that way -- or whether it is the right track.