President Carter's struggle to bring the huge federal bureaucracy under control is being watched with sympathy in Britain, for the present climate here is more favorable to pruning the civil service than it has been sillce World War II. The key question, however, is whether rising public impatience will be sufficient to stimulate reform.

Ordinary voters, caught between inflation and the government's freeze on wages, are in revolt against high taxes, even though British taxes are not particularly high by international standards. Commentators have tended to adopt the view that Britain's economy slid into its present hardships through waste and too much government, while private industry is widely believed to be short of capital because of excessive public spending. And finally, the government itself is grappling with the impact of a [WORD ILLEGIBLE] squeeze on the budget, imposed late last year the International Monetary Fund as its [WORD ILLEGIBLE] a $39-billion loan designed to bail out Britain

At this then, accounts for the tremendous amount of talls and even effort being concentrated on looping off some of the bureaucracy's [WORD ILLEGIBLE] But the trouble, as usual, is that the bureaucratic monster has regenerative powers: It can grow three new limbs for every one removed.

In 1961, for example, the public sector of the British economy employed 5.8 million people, or 24 per cent of the nation's active labor force.

Last year, after a decade and a half of constant reductions, the figure had risen to 7.5 million, or nearly 30 per cent. An explanation of the statistics shows what happened.

One of the largest bureaucratic increases has taken place in local government, where the number of men and women employed has soared in the past 15 years from 1.8 million to more than 3 million.

This has occurred because city and county authorities have the right to hire without interference from the central government, which can only exert indirect pressure on their payrolls. This pressure is ineffective, however, since the local authorities can finance themselves by boosting real-estate taxes.

It is also difficult to discipline the nationalized industries, which today account for some 2 million employees. Some major government owned industries, like coal, steel and the railroads, have in fact shed manpower in recent years as a consequence of improved productivity. But a jungle of smaller public enterprises, such as regional water agencies and civil aviation departments, proliferates freely.

The armed forces have been shrunk within the last 15 years, mainly because successive Labor Party governments have been retreating from overseas commitments. But the central civilian bureaucracy has spiraled within the same period from 1.3 million to more than 3 million employees.

Much of this growth has been in the bureaus that handle taxation and in the field of social welfare, which deals with a complicated range of health, unemployment, old-age and other benefits. Even so, it is doubtful that so many new jobs are necessary for the additional tasks.

In a public service such as the police department, the supporting staff has expanded by a far higher proportion than the front-line troops. Within the past decade, the number of police has increased by 26 per cent while the number of clerks and other bureaucrats has gone up 89 per cent. The same is true of the fire department, which has taken on twice as many deskbound employees as it has firefighters.

British politicians have concluded that economizing is not just a matter of curbing domestic responsibilities or simplifying the fiscal and social-security systems, but could be achieved through tighter management. To this end, the government decided last fall to pare the civil service and thereby save about $250 million.

But the bureaucrats, supported by their powerful labor unions, displayed real ferocity. They contended that thinning their ranks would damage their capacity to provide the public with social welfare, and after a good deal of haggling, they won a partial victory. Part of the appropriation removed from their budget was restored, and, as the bargaining continues, it is expected that more will be restored.

Meanwhile, studies have been initiated to calculate the effect of the potential bureaucratic cuts on the operations of the bureaucracy. And these studies, of course, must be considered by bureaucrats . . .