The deeper you delve into the Falkland Islands confrontation in "war"-torn London, the better your understanding of why Secretary of State Alexander Haig is doing what he's doing, in exactly the way that he's doing it--high-wire diplomacy at high speed and high risk, without a net. He is doing it that way because, in the last analysis, that's the way British Prime Minister Margaret Thatcher wanted it. In some American quarters it may look crazy-wild, or self-serving. All about you, here there are Tory roars: opposition politicians and the tabloid press cry out against the first hint, in American honest brokerage, of betrayal of an old ally, of treacherous "neutrality."

"Outside the British government," says the Daily Telegraph, "Uncle Sam has probably not been so unpopular in this country for a long time." But "outside" is the operative word. With the handful of people in the upper reaches of government who know what's going on, it's an altogether different story, and one worth looking into as politicians and commentators in the United States clamor for Haig to slow down or "stay home" or set up some nice, quiet peace conference that would free the United States to find its natural place in the British camp. To comprehend the Haig mission you have to begin at its beginnings: the rancorous, recriminatory, fire-eating first special session of the House of Commons on April 3, the day after the Argentine assault. Nobody was quite prepared for the intensity of feelings welling up. Even Thatcher was shaken--"shocked out of her shoes," was the way one intimate put it.

She had to handle it herself, and not just because her government was at risk: her trusted foreign minister, Lord Carrington, had resigned, and she could hardly delegate authority to the man picked as his successor, Francis Pym, her chief opponent and likely successor if the mission fails. So it had to be high, which is to say Haig, level. And it had to be fast. Time--even the time it would take the fleet to reach the war zone--was not on her side. Patient diplomacy did not fit the public mood, not then and not now, even though the first jingoistic outbursts are giving way to more judicious second thoughts.

The Thatcher government frowns on the Reagan administration's strategic infatuation with Argentina, but it will tolerate it for as long as "evenhandedness" shows hope of a tolerable settlement. It understands the nature of Haig's awkward straddle and appreciates the effort. But it is quite ready to insist that U.S. neutrality be abandoned in favor of full backing for Britain if, as the fleet closes on the Falklands, mediation shows no reasonable prospect of progress.

The British want to win. But they would rather use their fleet for diplomatic leverage than for an invasion of the Falklands that might cost more lives than it would save from Argentine occupation. Now that, you might say, is wanting it both ways--and you would be right. "It's a set-up," says one insider in a position to know how Haig got involved, but he adds: "Al knew that when he took it on. The stakes were too big not to try." So it's a heavy gamble. But it is not, as a lot of Americans as well as British would have you think, the mark of a faithless ally.