Labour and unions square off against Prime Minister Thatcher

British trade unions, once famed for their militancy, have been losing members, funds, and battles with management in recent years. With 3 million pople here out of work, with Conservative Prime Minister Margaret Thatcher reelected last June with a 140-seat majority, and with government legislation pending to cut union power even more, union leaders talked of the need to show a ''new realism.''

But now unions and the opposition Labour Party, which unions largely finance, see a golden new opportunity to reassert their influence.

It takes the form of a growing dispute over the government's decision in January to strip union membership from civil servants at the top-secret Government Communications Headquarters (GCHQ). The workers intercept Soviet and other satellite and ''signal intelligence'' and send the data to Washington for NATO analysis. Some reports say they eavesdrop on allied commercial and private telephone and telecommunications traffic as well.

The government says union members disrupted collection of the data in 1981 when they went on strike for higher pay. This, it argues, affects national security.

Washington is said to agree. US intelligence officials are said to have exerted strong backstage pressure to ban unions from GCHQ after the 1981 strike.

US fears grew when a GCHQ Russian linquist, Geoffrey Prime, was convicted of spying for the Russians. Washington has provided a number of lie detectors to use on British intelligence workers.

Unions reply that their members are loyal to their country, and they have offered a virtual no-strike pledge if the government will back down.

Many union members say they are afraid the prime minister, with her large majority, is preparing further punitive actions against unions in general. Employment Minister Thomas King says this is not true.

Labour Party leader Neil Kinnock portrays the government as complacent and slipshod. Government officials themselves concede privately that the GCHQ issue has been badly handled within the government and that it was kept secret for too long.

But they say the prime minister still believes that intelligence workers who belong to a union have divided loyalties.

Current national union strategy is to widen the dispute and put pressure on the government.

Many observers doubt that the ''new realism'' will fade entirely. Underlying economic factors that are weakening the unions are still strong.

But for the moment, the Trades Union Congress (TUC) has:

* Called a half-day national strike Tuesday that disrupted rail travel, ambulance and fire protection, customs and other services, especially in Scotland, Liverpool, and London.

* Threatened to withdraw from bodies such as the National Economic Development Council and others handling arbitration, employment, and health and safety.

Veteran labor observers see this as a shrewd game of union bluff to try to force the government to back down on the GCHQ issue. They doubt the TUC can, in fact, withdraw from government bodies on health and safety, for instance.

The union pledge not to strike has been supported by a House of Commons select committee. It reported that the government should freeze its no-union plan while trying to work out an acceptable no-strike pledge from the unions.

A former head of GCHQ, who drew up the original plan now adopted by Mrs. Thatcher, told the committee he would have dropped the plan and accepted the pledge already offered by civil service unions.

At time of writing, the prime minister was standing firm. She claimed most GCHQ workers had already agreed to leave their unions.

Mr. King said Monday that almost three-quarters had done so.

If the government sacks the other 25 percent, unions say GCHQ work will be hurt anyway.

Intelligence data needs to be collected around the clock, seven days a week. Union leaders admit that collection was severely interrupted during the 1981 strike but insist that ''basic services'' were maintained.

Mrs Thatcher is unimpressed.

Meanwhile Employment Minister King scored a recent success with unions by negotiating an agreement over how union members can pay, or not pay, political levies to the Labour Party.