Why has British Foreign Secretary Geoffrey Howe been launched on what looks like a "Mission Impossible" in search of a diplomatic breakthrough to end the evil of apartheid in South Africa? A short answer is that his prime minister, Margaret Thatcher, will do anything to delay the day of decision on tough economic sanctions against the Botha government.

The same put-down is as easily applied to the Reagan administration's well-publicized "shift in emphasis" to strike up closer relations with black leaders and antiapartheid whites in South Africa. And an equally cynical motive can be read into reports from Bonn that West German Chancellor Helmut Kohl is under heavy pressure, even from within his own party, to propose a "Summit Impossible." It would include Botha, the leaders of the outlawed African National Congress, South Africa's neighboring, black "front-line" states, as well as Britain, the United States and West Germany, which have the largest economic involvement in South Africa -- and the most to lose in any general application of economic sanctions.

A high-ranking British official expresses what would seem to be the guiding spirit: "We must be seen to be doing something." But nothing too harsh or too hasty, it would appear. Self-serving commercial, economic and political imperatives are overriding considerations. Thatcher's critics shout "Munich" and cry out against the hypocrisy of it all.

Well, maybe that's what we are witnessing in the measures under way or under consideration by those Western powers able to exert the greatest influence against apartheid's cruel repression: a great cop-out. But unless you are confident that the main parties at interest -- the United States, the European Community, the British Commonwealth (whose far-flung 49 members include a fair number of black African states) -- could ever agree on a comprehensive sanctions policy that would do more good than harm, allowance must be made for a second opinion.

Call it the Thatcher Opinion, and not only because she is its most resolutely opinionated proponent. She is better placed than any of the other key players to play a decisive role. She has, for example, the best connection with Ronald Reagan, whose distaste for sanctions nearly matches hers. Britain has just assumed the rotating, six-months' presidency of the European Community Council, where Thatcher has another kindred spirit of like mind on sanctions: West Germany's Kohl. Thatcher is the senior statesman among the leaders of the seven largest Western industrial states, whose annual summit meetings give them some clout on economic issues. And she has the weight of British custody, so to speak, of the Commonwealth.

That said, you have only to note the nearly mutinous mood of black African Commonwealth members, the challenge Ronald Reagan faces from sanctions advocates in the U.S. Congress, the rumblings of discontent from the European Community and the opposition uproar in the House of Commons to appreciate that Thatcher's position is as precarious as it is pivotal. She cannot make a common sanctions policy. But she may be capable of breaking one.

For she is in a Falklands mode, painting herself almost daily into a tighter corner, scathing in defense of her position, scornful of her opponents. If she has left herself any dignified line of retreat, it is in her careful distinction between general "punitive sanctions" and economic measures that are mere "gestures" or "signals" of the outside world's revulsion at apartheid.

She could, then, fall back to such further measures as those already imposed: arms sales, government-to-government loans, recall of military attach'es, a ban on buying gold coins or selling computers to South Africa security forces. But she "totally rejects" the argument that even black leaders in South Africa and the "front-line" states are ready to accept far tougher measures at the cost of greater economic distress for their own impoverished people.

Against the immorality of apartheid she casts the immorality in southern Africa of throwing blacks out of work and depriving starving children of food -- while also bringing economic hardship on her own people by the application of measures that will not work. She finds that "utterly repugnant" or "absolutely absurd."

She foresees the South African government hardening, not softening, in its resistance to change, while inflicting heavy reprisals on "front-line" states whose economies are vulnerable by their economic dependency on South Africa. She is appalled at the thought of banning purchase of strategic minerals from South Africa when the principal alternative source -- and the certain beneficiary -- is the Soviet Union.

She was reminded in a recent interview that she had once said, "If I were the odd one out and I were right, it wouldn't matter, would it?" The obvious answer is that it might matter a lot. But there is weight to the evidence thrust upon a visitor to No. 10 Downing Street: the past experience with "punitive" sanctions, the detailed economic data, the dogged intransigence of Afrikaners in the face of outside pressure, and the modest, slow reform already achieved. It is enough to make you wonder whether she might be right.