London — Some recent headlines tell the story: ''Vote at Unilever to end union pay role ''; ''BL (British Leyland) strikers in Glasgow defy shop stewards and return to work today.''
These are indications that Britain's trade unions are in trouble. Whether entirely fair or not, they are renowned worldwide for being tough, old-fashioned , keen on featherbedding - and for resisting technological progress and being prone to strikes and jurisdictional disputes. But they have been badly weakened by ''Thatcherism'' and this nation's unemployment rate of more than 13 percent.
With it likely that Margaret Thatcher will be reelected Thursday with increased strength in Parliament, it could be that the unions are being permanently tamed - that even with recovery and full employment, they will be less able to disrupt industry or the nation, even forcing governments out of power.
''It may be this is the last struggle,'' says Allen Budd, an economics professor at the London Business School. ''We may permanently win the battle with the unions.''
Through Employment Acts in 1980 and 1982, the government imposed new legal constraints on the labor unions' power. The first limits ''secondary picketing'' by unions not directly involved in a dispute and allows companies to obtain court injunctions against such strikes. It also provides state aid for secret employee ballots. The second act increases protection for employees dismissed for nonmembership in a union. It also removes legal protection for closed shops (where only union members can be hired by a firm) and voids contracts requiring use of union labor only.
Further, the Conservative platform promises to give union members the right to:
* ''Hold ballots for the election of governing bodies of trade unions.
* ''Decide periodically whether their unions should have party political funds.''
Norman Tebbit, the employment secretary, has expanded on changes the Tory's are planning if reelected. Unions would have to hold a strike ballot - ''fair and free'' - before calling either a local or national strike. If there were no ballot, the union could lose its legal immunities against being sued.
Further, union members would be given ''an effective choice'' on whether their union dues could go into a political fund that is used to support the Labor Party. One possibility, Mr. Tebbit indicated, would be to require the union member to agree to such a political use of his money - rather than for him or her to formally request not to pay to a political fund, as is necessary today. Since the Labor Party relies heavily on union contributions, this has major political implications. Mr. Tebbit told the Financial Times, ''. . . We wouldn't want to wreck a political party lightly.''
Tory politicians maintain that such actions are not in themselves just for the sake of ''union bashing,'' as the British put it. They want to prevent the unions from stopping the shrinking of old, overmanned, inefficient industries and the moving of manpower to new services and new technologies.
''Tragically, trade unions have often obstructed these changes,'' the Conservative platform says. ''All too often this has delayed and reduced the new and better-paid jobs which could replace those lost.''
During the current severe recession, management has been able to impose massive changes in work rules and other efficiency measures. Organized labor often has been too weak to resist. Time lost to strikes has dropped to extremely low levels. Total union membership declined from 10.1 million in 1979 to 9.3 million in 1982.
Union leadership has often been out of step with the rank and file. Members will often accept a low wage settlement and vote against their leaders' strike orders. The most startling case was when coal miners voted overwhelmingly against the strikes urged by Arthur Scargill, the Marxist president of the National Union of Mineworkers, in November 1982 and again in March of this year.
The government has also won pay showdowns against BL Ltd (formerly British Leyland, the automakers), public health service employees, British Rail, and British Steel. In private industry, managements' backs have been stiffened by the knowledge that the Thatcher government is not about to bail them out with subsidies. Executives in the nationalized companies are under clear instructions to reduce the need for subsidies.
All this has resulted in a major shakeout of labor from overmanned industries in the last three years, a development that is partially responsible for the current 13.6 percent unemployment rate and rapid increases in productivity. But will labor and management work out a new relationship that will permit further productivity gains in the future? Or will the trade unions insist on going back to the old ways once anything like a labor shortage appears?
Dr. G. Brian Henry, director of research, National Institute of Economic and Social Research, suspects the shakeout of labor is reversible - that productivity gains larger than ''normal'' will not be continued once an expansion begins. ''I can't see the degree of trust in the British labor scene for that to happen. But if we go back largely to the old manning, then the whole effort has been wasted.''
Nor does Willem Buiter, an economist at the London School of Economics, detect ''a massive change in the hearts and minds on the shop floor and among management. In some ways, British industry is the home of inefficiency.''
However, he does foresee some change toward a more rational management-labor relationship. ''The recession has concentrated people's minds,'' he said.
According to Prof. Allen Budd of the London Business School, much of British management remains ''ill trained and technically poor.'' But management schools have been teaching modern management for years, and their graduates are now reaching higher levels in companies. These younger executives are more likely to have an ideal of working as a team with their employees to make corporate progress.
One impediment to a change in attitude are the remnants of the class structure. Collective bargaining is often felt to be a battle between classes as well as between management and labor. ''A lot of workers resent management,'' Mr. Budd said. ''It is very difficult for the work force to identify itself with the company. That is management's fault as much as labor's.''
Many executives still are horrified at the idea that workers should have anything to do with management. ''There are the leaders and the led, the managers and the managed, the officers and the men - this is such a strong element in the British system,'' Professor Budd added. ''It leads to deference and resentment.''
But this system is breaking down. ''I don't think this class structure exists except in imagination,'' said Timothy H. Bevan, chairman of Barclays Bank. ''Britain is much more of a meritocracy today.''
However, most observers would argue that Britain's class structure has not yet fully disappeared. Nor have workers and management sufficiently mended their sharp split. According to Professor Budd, the next four or five years of likely Tory rule, combined with the weakness of the Labor Party and the decline in socialism, may further teach the lesson that a higher standard of living requires improved productivity and better management-labor relations.
Next: lessons in monetary policy.