BRITAIN'S CONDITION ought to be a matter of sharp concern to the theorists of the American left--if there still is an American left, and if it still has any theorists. Currently, the analogy between this country and Britain is mainly fueling the quarrels over economic policy within the Reagan administration. But the analogy isn't a close one. The British economy is very different from this country's. Because of the nationalized industries-- steel, autos, coal, power and the rest--its public sector is much larger. That's the question that British experience presents to the strategists of the left: how does a democratic government conduct economic policy in a country with large government- owned companies and a militant labor tradition?

Until recently, most people supposed that government ownership at least made it easier to maintain public control over prices and wages. Whatever the losses in efficiency, the argument went, nationalization made an incomes policy manageable. But that's the surprise of the past decade--Britain's enormous inflation rate.

The persistence of rapid inflation, in the midst of a profound recession, is often cited as proof of the failure of Prime Minister Margaret Thatcher's monetarist policy. It might better be cited as proof of the intractability of the nationalized industries.

In those industries, a strike is not an economic weapon against one company but a direct political challenge to the government. Even the Thatcher government has been able to withstand only a limited amount of that sort of thing. The result has been poor control over wages in the companies where it theoretically has the best and closest control--those that it runs directly. With the British unemployment rate now over 11 percent, things may be changing a little. The management of BL, the national automobile company, has apparently faced down the most recent threat of a strike. But it had to resort to a counter-threat to let the company collapse.

Mrs. Thatcher's struggle against inflation has been fairly successful in the private sector. It's the public sector that's doing her in. To get the public deficit down, she has repeatedly had to let the government's companies raise prices. Prices in the public sector have been rising several times as fast as in private business.

Radical politics very often leads to conservative economics--conservative in the sense of resisting change. Most people are pretty conservative about the ways in which they earn their livings. Faced with a plant closing, nobody is much consoled by the thought that it's the price of growth, and that some other plant with higher productivity and better wages will eventually spring up somewhere else. But there's a heavy cost exacted by the unconditional preservation of jobs in uncompetitive and obsolescent factories. Not all of the examples are British. These are choices that Americans are going to have to make, if the current tremendous losses continue in this country's automobile industry.