THE BRITISH government has now ordered a retreat from its strategy of extremely high interest rates. The retreat is only tactical and partial, but it's a warning to those Americans who truly believe in monetary theory and its creed that a modern economy can be controlled through the money supply alone. The government had intended to reduce interest only as it succeeded in braking the expansion of the money supply. In fact, the government is now reducing the rates because of rising unemployment and deep distress among British businesses -- especially the most competitive ones that produce for the export markets.

For the monetary agnostics -- those dubious pragmatists who find monetary ideas interesting but not quite persuasive -- there's a further lesson. For all of its monetary fervor, the Conservative government under Margaret Thatcher has been led to exactly the same place to which much more conventional policy has led the American government under Jimmy Carter. The British forced interest as high as they dared, and still the money supply expanded too fast. The only other way to restrain it is to reduce public borrowing -- that is, cut the budget deficits.

That's what the British government is struggling to do now, with new spending cuts and higher taxes, and that's what the Carter administration has been trying to do since last March. Meanwhile, the American government -- which doesn't really believe in monetary theory at all -- has gloomily raised interest again as a stopgap to buy a little time until the new Reagan administration takes over.

The British experience is full of instruction for Americans. At one point, Mrs. Thatcher's government resorted to the manipulation of the banking system in its attempt to squeeze off the creation of new loans. It imposed a limit, known as the "corset," on bank credit. London's highly sophisticated financial houses responded by arranging loans outside the banking system, directly between borrowers and lenders.

Controlling the money supply, except through high interest rates, turns out to be nearly impossible in an advanced economy. Money, after all, is anything that lenders will accept, including all sorts of commercial IOUs. Anybody can create it; and bankers' ingenuity always runs ahead of governments' controls.

The purpose of the British experiment was to end the era of high inflation by tight restraint of the money supply. When there was no more money, it followed that there would be no more wage increases. Now as always, the British struggle against inflation depends mainly on the government's ability to hold down wages in the public sector -- especially in the nationalized industries like coal, steel and automobiles. While the monetary strategy has proved a disappointment to its designers, a tough and determined government may yet prevail on the main question. That was never a matter of theory, but of whether Britain can actually end a long and corrosive cycle of rapid inflation.