Britain has much to offer the American election campaign.

In 1976 we figured prominently, with Gerald Ford campaigning under the slogan, "Don't follow England down the drain!" This year the Republicans have decided they have other sorts of lessons to learn from us. Hard-nosed men with horn-rimmed eyes (let alone glasses) have crossed the Atlantic to make admiring studies of how the battle of Britain of May '79 was won. They return home, one is told, to apply the gospel according to Thatcher with a terrible and scientific rigor.

The wonderful humorlessness of their effort is excusable, no doubt, by the stern nobility of their cause: to bring about a conversative resurrection of strong leadership and thereby to restore the full bloom of American greatness. sTo be fair, it's not a party matter. If Teddy, Jimmy, Ronald and all the rest have one thing in common it is an overriding obession with "leadership" and greatness."

What Americans get instead are crooked lawyers, men who play football without their helmets, blumbling peanut farmers or washed-up film actors.

The real task ahead of the American political elite is exactly the same as our rulers faced in 1962. They must, above all, face facts. The United States made up half the capitalist world economy in 1945, but only one third of it now. By the year 2000 it will constitute less than a fifth.

These figures alone spell out quite definitively the end of the "American century." Nothing is more certain than the collapes of the dollar as the world reserve currency, or the gradual abolition of all the other economic privileges which the period of hegemony brought. To take the most obvious: American industry must look forward to the day when it must compete against foreign exporters without the benefit of a huge subsidy in the form of the world's cheapest energy.

They must expect, moreover, to have to do this while undergoing a variety of political harassments around the world, as former client states vent their long pent-up resentments against the weakening giant. A lot more embassies will be burned down and, probably, a lot more hostages seized. They must, finally, not expect their allies to rally round them as they undergo this slow crucifixion.

Having faced all of these somewhat uncomfortable facts, the really major task will be to manage the imperial run-down as smoothly as possible and "sell" its consequences to the American electorate. This will involve a large-scale lowering of public expectations and something approaching an admission of historical guilt. It will be necessary to explain that these trying situations at the Tehran embassy and elsewhere have much deeper causes than are to be found in any immediate situtation.

Just as at Suez the British were picking up a Late bill for 100 years of colonialism, so the Tehran hostages now are paying for CIA supoport of SAVAK, for the deposing of Mossadeq and much more.

All of this will be much harder in the American case than it was for the British, for two reasons. First, the bonds of American empire were always largely invisible to the public at large. This means that there is no formal process of decolonization to conduct, through which your electorate gets the point by seeing the flag hauled down in one colony after another. Secondly, no successor imperial power is in sight.

It was a great help to the British elite in its age of decline to be able to lean on the strong supporting arm of the "special relationship" with the new giant who -- what luck -- even spoke English and was willing make occasional respectful gestures to the old lady. The United States won't have this -- merely a lot of Germans, Japanese, South Koreans and others, all competing fiercely with it one ever more equal terms.

It will be seen that if ever the time existed when the British might play their cherished role of Greeks to the American Romans, now is that time. The counsel we should give is plain. For heaven's sake avoid our mistakes. Cut your losses. Don't do the equivalent of decolonizing India in 1947 and still find yourself mucking around the Rhodesia in 1980. Avoid, at all costs, any talk about "greatness." And don't fall into the trap of thinking that a conservative reaction can save you. Your empire declined faster under Nixon and Ford than under anyone else, and Reagan would be no different.