"WHO are WE?"

That the queen has probably never exercised her royal prerogative to raise so elementary a question with her prime minister, Margaret Thatcher, in one of their regular weekly chats is of no moment. The question is ever-present here. It colors every conversation with Britons of all sorts. It leaps out of public-opinion polls.

It is encapsulated in the bitter British debate over South Africa, with Thatcher presenting herself as the senior statesman of the Western World, making global waves while her opposition worries over Britain's being odd man out.

The same question compounds, more broadly, the deep divisions within the ruling Conservative Party and within the opposition -- as well as the warfare between them. More so than at any time since World War II, the British are in the grip of an identity crisis.

The roots run to the collapse of empire and to Britain's protracted game-playing in the formative years of the European Community, before finally joining up (the early ambivalence lingers on); they run to the value placed by some, including Thatcher, on a cherished "special relationship" with America and an independent British nuclear capability, and the resentment felt by others about British dependency on Washington's will and whim.

To these tugs and hauls add the Commonwealth connection, and you have the makings of something on the nature of a national nervous breakdown with various consequences for American foreign policy. The symptoms are everywhere:

The immediate worry over what Thatcher's opposition to wide-scale "punitive" sanctions against South Africa is doing to the Commonwealth Games in Edinburgh. A few proud Britons may resent the impertinence, but most would deplore lasting damage to the Commonwealth itself -- and none more so, one surmises, than the queen who presides over it. When the queen, as Victoria would have it, is not amused, the Briton on the street is not amused.

The recent flaps over Westland and Leyland, the former a foundering British helicopter manufacturer and the latter a troubled builder of automobiles. Without laboring the details, the issue in both cases turned on the pros and cons of bailouts or takeovers by American firms. As one U.S. diplomat puts it, "Westland and Leyland stirred up the whole question of dependency on America."

The use of bases in Britain for the U.S. air strike on Libya, coming hard on the heels of Westland/Leyland. "The stage was already set for a critical reexamination of the relationship with us," says another American official. And the public judgment of Thatcher's acquiescence in the Libyan air strike was overwhelmingly critical. The taunt that Thatcher is Reagan's "pet poodle" has become a fixture in the cries of the opposition in parliamentary debate.

The swarms of antinuclear protesters in the halls of Westminster. The nuclear disarmament movement is louder than it is large, but it is the cutting edge of a public disinclination to depend on the United States for British security. The resulting contradictions make no sense: the opposition Labor Party sounds as if it is wedded to unilateral nuclear disarmament and denying base rights to the United States -- as if this could be somehow compatible with membership in NATO, whose strategy of deterrence is calculated on the availability of British nuclear forces and U.S. base rights in Britain.

A paradox of the "anti-Americanism" in public-opinion polls. A large majority "like" Americans, according to a recent study by Market and Opinion Research International. What they definitely don't like, by even larger majorities, MORI found, is excessive American influence over British industry or the economy or defense policy or morality and television.

Even worse, considerable majorities questioned Ronald Reagan's judgment and doubted he could be "trusted to look after British interests." Astonishingly, one out of five rated the United States a bigger threat to the peace than the Soviet Union, and one-third saw nothing to choose between the two.

Ordinarily the electorate would clear the air, and a general election will be held no later than 1988. But the fluctuating polls, now showing Labor with a chance for a working parliamentary majority, more often show a roughly three-way split between Labor, Conservatives and the five-year-old Alliance (a loose partnership between the old Liberal Party and a new splinter group of disaffected Laborites).

A clear Labor majority could have a transforming effect on Britain's international relationships, special or otherwise, but that's not to say it would crystallize a new British sense of identity. If the United Kingdom cannot figure out what it is -- or wants to be -- after seven years of rule by a steely prime minister with a mammoth parliamentary majority, you have to wonder how long it will be or what will have to happen before it can.