Can Britain catch up with Germany?

The race is on. Nigel Lawson, British chancellor of the Exchequer, says his country has ''a very good chance'' of catching up economically with West Germany.

Contrariwise, German Finance Minister Gerhard Stoltenberg, while welcoming the ''strong improvement in the British economy,'' notes, ''We are about on the same track now. The latest figures are very good.''

The United Kingdom and West Germany are no longer military antagonists; indeed they are firm allies. But a sense of economic rivalry has remained. Until recently, Britain was falling far behind in the friendly post-World War II economic marathon.

Mr. Lawson maintained in an interview here that Britain now has economic policies ''which give us the basis for catching up.'' He noted that the UK has enjoyed three years of something like 6 percent annual growth in manufacturing productivity.

''This has been achieved in part by getting rid of overmanning,'' he said. ''The recession forced British industrialists to sharpen up.''

Mr. Stoltenberg, at a breakfast meeting, predicted that the West German economy would grow this year about 2.5 per-cent, somewhat lower than the 3 percent expected earlier because of a metalworkers strike this spring.

''The German economy is much better than the image abroad,'' chipped in Karl Otto Pohl, head of the German Bundesbank, who was also present at the breakfast. He maintained that Germany's exports remain highly competitive. West Germany has a bigger volume of exports of industrial equipment than the United States or Japan, and, though he didn't say so directly, than Britain.

Mr. Pohl added that West Germany has lower inflation than Switzerland or Japan. (It also is less than that of the UK - under 3 percent compared to about 5 percent.)

The British economy, like Germany's, has been hit by a strike. But unlike the German metalworkers, who went back to work after seven weeks, the British mineworkers are still on strike after six months. Thus British output should grow ''closer to 2 percent than the 3 percent previously expected,'' said the chancellor of the Exchequer.

Mr. Lawson offered a number of other reasons why he sees Britain ''catching up gradually a lot of the ground we have lost.''

* The balance of payments is no longer the acute worry it was in the past. In the days of fixed exchange rates, it often forced Britain to put on the economic brakes.

North Sea oil ''has obviously made a difference,'' he said.

* The government is ''bringing trade union attitudes into the modern world. There is a great deal more realism on the shop floor. It is not just a matter of legislation, though we have introduced three different stages of legislation.''

* Business profitability, declining since at least the 1960s, now is rising.

''The low return on capital ... really affects the animal spirits of businessmen in an adverse way,'' Lawson said.

* Management quality has improved. ''There is a very different climate from five years ago.''

The chancellor was cautious not to claim complete victory over the business cycle. But he did point out that the British economic recovery was in its fourth year ''with no signs of it petering out.''

He gave prime credit for this to his government's monetarist credit policy, which has aimed at gradual reduction in the supply of new money to bring down inflation.

''There is a lot more to it than that, though,'' he said. ''We also believe in keeping the budget deficit down. So you could say we believe in fiscalism as well as monetarism.''

Lawson's budget calls for a deficit this year equivalent to 2.25 percent of national output, compared to more than 3 percent last year. The US federal deficit, even if state and local budget surpluses are subtracted, remains higher as a proportion of gross national product, he claimed.

Lawson boasted about other government efforts to boost the ''supply side'' of Britain's economy, thereby allowing markets to work better and stimulating growth. He cited deregulation of industry; elimination of controls on foreign exchange, dividends, pay levels, prices, and so on; a reduction in some income tax rates; denationalization of government-owned industry; and increasing competition.

Another successful effort of the government of Prime Minister Margaret Thatcher, he said, is to reduce government spending as a proportion of total output. This ratio remains over 40 percent in Britain, compared to around 30 percent in the US, he figured.

Such reforms, he said, should make the British economy vigorous, as in the US. This vitality ''enables you to bounce back from a recession very much more dramatically than we have.''

Partially because of these reforms, there are already ''a lot of exciting things happening'' in British industry, he held.

Lawson admits that high unemployment remains a severe problem in Britain. But he argues that reforms that have been made so far should result in business creating more new jobs and bringing the jobless rate down.

He looks to ''no tech'' jobs in the service industries to provide more positions than high-tech industry.

But he says there is little prospect of reversing the unemployment trend unless Britain can moderate the growth of real wages. In Britain, after removing the impact of inflation, pay levels rose throughout the past recession and the current recovery. In the US, real wages have been relatively stagnant. Economists argue that when labor is more expensive, business hires fewer new workers.

But can the government persuade the working public that the rise in their living standards should slow down?

Lawson replied: ''One of the things politicians tend to do is underestimate the common sense of the people. People don't think the world is a world of endless goodies. If they have a government which tells them the truth, they are prepared to respect what is said and accept what is said far more readily than many governments in the past have imagined.''

There is, he went on, an overlap between what is politically possible and what is economically necessary. The return of his government to power in elections last year proves that, he maintained.