Prime Minister Margaret Thatcher and her chief economic lieutenants are mapping strategy for an all-out effort to hold down government and industry pay increases that could provoke a major battle with Britain's labor unions next winter.

With both inflation and average wage increases still hovering around 20 percent despite her Conservative government's tight money policies, Thatcher wants to hold pay raises well below the inflation rate in the annual wage bargaining round beginning in the autumn.

She is particularly determined to hold down government workers' pay as an example for private industry. Many employers, squeezed by both Thatcher's monetary policies and the deepening recession here, also are ready to take a tougher line in wage bargaining next autumn and winter.

This is widely expected to produce a long-waited confrontation between Thatcher and the unions, whose leaders have warned that they cannot agree to substantial reductions in workers' standards of living. Thatcher's candid treasury minister, John Biffen, has forecast "a protracted winter of discontent."

"There is no doubt that the coming pay round will provide a critical and possibly decisive test of the government's strategy," declared stockbrokers and economic analysts Phillips and Drew in their latest economic forecast for Britain. "Another round of 20 percent settlements would eliminate much hope of a major immprovement in the inflation rate next year, would jeopardize the government's fiscal and mometary targets, and would greatly deepen the 1981 recession."

Chancellor of the Exchequer Geoffrey Howe has pointed out that Britain is the only major industrial nation whose workers have not allowed their pay to fall behind soaring inflation in recent years. Lord Soames, Thatcher's minister for civil service, warned this week that wage settlements must now be determined by the government's and private employers' ability to pay rather than by inflation.

Thatcher, who has been discussing with her economic ministers since mid-May ways to hold down pay raises during the coming wage round, has warned that "the government must set an example. We cannot and will not let public sector pay become the peacemaker for inflation."

Government employe union leaders have vowed to stand their ground, and Britain's top labor leader, Len Murray, general secretary of the Traders Union Congress, has refused entreaties that the unions moderate their wage claims to fight inflation.

"As long as price increases are there, working men and women will have to respond and seek to defend, as best they can, their living standards," he said this week. "No one enjoys inflation at 21 to 22 percent, but it is nonsense talking about wage restraint in these circumstances."

As Thatcher knows, public opinion polls show the unions have been unpopular with the British public since the widesprpead winter strikes by truckers and government workers in early 1979, which helped defeat Thatcher's Labor Party predecessor, James Callaghan, as prime minister. The gamble she and her advisers are now weighing is whether her government or the unions would suffer the most blame if protracted confrontation over pay produced another winter of conflict.