Could yesterday's crash in the London stock market be an advance warning for President Reagan?

The British and American economies are very different, and it is hard to imagine a recession here as deep as that now being experienced in Britain. But Reagan's pronouncements on economic policy bear a striking resemblance to those of Prime Minister Margaret Thatcher two years earlier.

British investors apparently have now decided that the desperately awaited economic upturn - which some of them thought they had glimpsed on the horizon this summer - is still too far off to be seen. After two years of slump, when unemployment has reached depression levels and many firms have gone out of business, the one bright spot in Britain had been a drop in inflation and in interest rates. The stock market this summer acted as if the bad times were over, or at any rate about to be.

But two weeks ago the Bank of England pushed interest rates up again, to shore up the faltering pound. Markets, which had believed that higher rates were ruled out politically, then woke up to the fact that Thatcher will keep policy tight as long as she believes that loosening risks worse inflation.

Unemployment is already at the 3 million level - with more than 11 percent of the adult work force out of a job - and is still rising. Output, though no longer falling, is at very depressed levels. The Confederation of British Industry's latest survey reported that well over half of the firms questioned expected no pickup in the economy in the foreseeable future. But the British government has put fighting inflation ahead of encouraging growth.

A fall in the pound generally feeds through quickly and damagingly to Britain's inflation rate. First, import prices, which are a major element in costs, push up the price level, and then wages usually rise to catch up.

The extraordinary strength of the pound until earlier this year was a major help in bringing inflation down from the level of more than 20 percent that it reached during Thatcher's first year in office to its present rate of about 10 percent. But since its February peak, sterling has dropped by more than 17 percent against the average exchange rates of its important trading partners. If unchecked, such a drop would be bound to reignite inflation.

Thatcher's commitment to fight inflation meant that interest rates had to rise to try to bolster the pound. But this return to high interest rates is also bound to put off Britain's recovery. As money market rates pushed up towards 16 percent last week, investors began to sell in earnest.

To the extent that they pull sterling back up, high rates will damage British industry twice over. The high pound has slashed British exports and made it harder for domestic firms to compete with imports in British markets. Sterling's slide was, therefore, good news for firms that hoped the slump in their sales had finally bottomed out.

British officials -- many of whom are here for the annual gathering of world finance ministers and central bank governors under the aegis of the International Monetary Fund and World Bank -- are blaming Reagan for much of their present difficulties. High U.S. interest rates, they say, are dragging up rates worldwide. Moreover, growing unease in Wall Street over Reagan's mix of tight money and looser fiscal policy has now spread overseas and made Britons gloomier about the long-term prospects for U.S. rates.

It is true that high U.S. interest rates may both slow the world economy and make the pound weaker. But the British government could choose a lower pound, lower interest rates and a risk of more inflation in order to give the economy some relief from recession. The lesson British markets have learned in the last two weeks is that if recovery begins, it is likely to run headlong into the government's tight money, anti-inflation policy.

Many analysts here fear that when the Reagan tax cuts begin to stimulate the economy next year, U.S. recovery may also run into a money crunch. The Federal Reserve is committed to very slow growth in the money supply, which, on past relationships, will leave little or no room for the economy to grow unless inflation subsides dramatically.

When Thatcher came into office she promised, as has Reagan, that inflation would come down swiftly, and the economy would grow, with the help of supply-side tax cuts to raise incentives. Early on, she had to choose whether to stay with her tight money policy, aimed at cutting inflation, or to ease up to avoid recession. She chose, and is still choosing, the first.

Reagan has not yet faced the choice. He is not likely to be confronted with such a grim one, as the U.S. economy shows no signs of crashing into a steep recession like Britain's. But American investors could still have some bad moments ahead.