THE BRITISH are fuming that the United States, in a vote on the Falklands issue at the United Nations, took the Argentine side. It's so. The issue was whether to support a resolution starting from the premise that sovereignty over the islands is unsettled and stating that it should be settled by negotiation. This is the traditional American position. It was the British position until last spring, when the Argentines, coming to the view that they had gotten nowhere in 17 years of talks, lost their collective head and invaded. But now the British, having expended several hundred lives and a billion or two dollars to regain the islands, hold that the wishes of the islanders -- British citizens all -- must come first.

This is, we think, an unfortunate position. It commits Britain, alone, to substantial garrison and development expenses. More important, it casts in concrete the Argentine grievance that led to the war and promises only trouble at some point down the road. Certainly, because of the Argentine aggression, the British are entitled to ask for extra guarantees. But to contend that the invasion altered either the historical or the political rationale for negotiating the sovereignty issue is wrong. Mrs. Thatcher is evidently still in the grip of Falklands fever.

The Reagan administration acted honorably during the crisis last spring, first by trying to mediate and then by casting the American lot with the British, victims of Argentine aggression. In that way the administration fully met its responsibilities to principle and to America's oldest ally. It was always clear, however, that after the war the United States would have to take steps to restore normal ties with Argentina and the many other Latin nations that had, politically, taken Argentina's side. When the British calm down, they will surely see that in the United Nations the United States reaffirmed the essential principle -- the peaceful settlement of disputes -- for which they went to war.