Britain's freshly reelected prime minister, Margaret Thatcher, blew through town the other day like a cool breeze: the perfect antidote for the humidity, the Iran-contra congressional hearings and just about anything else that might be troubling a beleaguered Reagan presidency.

To hear her tell it as she departed the White House after lunch with the president, and on TV talk shows, Ronald Reagan has never been in better form or better positioned to exert the power and influence of the United States on the world scene at a time of ''unprecedented opportunity.'' Even during ''this difficult period'' (her delicate reference to the Iran-contra exposures), ''he has not let go his leadership role in any way.''

But what, she was asked, about the polls and all the other political sounds in Europe, the Middle East and elsewhere that suggest ''weakened'' credibility and command? Nurse Thatcher would have none of it: ''I have absolute trust in him. . . . Cheer up! . . . The president's fine.''

Is that not laying it on a little thick? Of course, that's what the president's handlers had in mind when the one-day visit was arranged. That's also what made the effusiveness of her pep talk so interesting. That she felt the need to lay it on so thick confirms, rather than contradicts, just about everything you hear or read about the way the Reagan administration is now perceived in foreign capitals.

It says as much about Thatcher's condition as Reagan's. It says even more, subliminally, about the debilitating impact that the arms-for-hostages deals with Iran, the hanky-panky with the profits, the covert, private bankrolling of the Nicaraguan contras and the general collapse of the foreign policy process has had -- and is likely to continue to have -- on Reagan's presidency.

The head of Britain's longest-running government is quite sufficiently savvy and sensitive to worldwide political mood swings to be hearing what others are hearing: that Reagan runs no better and sometimes worse than Mikhail Gorbachev in European popularity polls; that the dealings with Iran have cracked the confidence of friendly Arab regimes, most notably in the Persian Gulf; that what interests foreign leaders increasingly is not what's going on now in Washington but who's coming next -- in 1989.

Thatcher also knows leadership when she sees it. ''The important thing is that you are consistent,'' she once said in her own defense. ''That people know exactly where they are with you, that . . . you do not dilly-dally . . . you discuss things with people, you submit your policies to them.'' Nothing there that would remind you of the picture emerging from the joint committee hearings of Ronald Reagan at work.

Thatcher knows the importance to Britain's place in the world of a close (but junior) partnership with whoever is in power in the United States. She knows that her fortunes for the first year and a half of her third term are linked to the fortunes of Ronald Reagan in the final year and a half of his last term.

It would, then, be a mistake not to examine her evidence, when Thatcher assures us that the president has not been ''deflected'' from the ''great matters which affect the world.'' Reagan had ''handled the South Korean matter,'' she said, which will almost certainly be news to the Koreans. The two leaders had seen eye to eye on the need to advance the Middle East peace process -- and never mind that the president gives no sign of sharing Thatcher's enthusiasm for an international peace conference.

It is equally hard to believe that Thatcher is as comfortable with the Reagan administration's naval escort service for Kuwaiti tankers as her exultations of his leadership in the Persian Gulf would imply. No sooner had she departed than her government shied away from a Kuwaiti request for a similar British ''reflagging'' operation.

The president, she said, has been ''very active'' on the matter of East-West relations and especially on arms control. But getting down to details, what she wished to convey was her concern over the absolute necessity for proper verification. ''We've got to get {the Euro-missile negotiations} right -- don't go for a quick settlement, get it right.''

She came to praise Ronald Reagan. But her own secure postion served somehow only to sharpen the contrast with the president's position -- like the visit of an excessively robust well-wisher to a sick room. Ironically, she came closer than the doom-sayers to burying the Reagan presidency by the urgency in her pleadings and the extravagance of her praise.