Less than halfway through its five-year term of office, Prime Minister Margaret Thatcher's Conservative government appears bogged down in Britain's deep economic recession and increasingly apprehensive about its political future.

Despite optimistic predictions by Thatcher and her chancellor of the exchequer, Sir Geoffrey Howe, the country remains at the bottom of the recession with output still declining and unemployment climbing to nearly 11 percent of the work force.

Economic analysts are forecasting that the recovery, when it finally begins later this year or next, will be painfully slow. Production is expected to remain lower and unemployment to be much higher by the time of the next national election in 1983 or 1984 than when Thatcher took office in 1979.

The reduction of inflation, which the Thatcher government has made its highest priority and claimed as its most promising achievement, also has slowed. After falling rapidly from a peak of 22 percent last summer to below 12 percent, the inflation rate is forecast to drop during the next year or two only to slightly below 10 percent -- about what it was before Thatcher became prime minister.

Thatcher's efforts to cut government spending continue to be thwarted by big increases in the cost of unemployment compensation and support for government-owned industries because of the severe recession. It appears increasingly unlikely that the government will be able to cut income taxes significantly before the next election, another top Thatcher priority and campaign promise. Instead, the tax burden is higher now than when she took office.

Thatcher and her chief economic ministers emerged from a gloomy, closed-door Cabinet reassessment of the government's economic strategy this week still determined to fight inflation with further attempts to cut government spending and restrict growth of the money supply, according to government sources.

But many of the signifcant number of Cabinet members who have long harbored doubts about this monetarist strategy reportedly expressed their growing misgivings about the damage they fear is being done to the country, particularly by high unemployment, and to the Conservatives' chances for reelection.

This autumn is seen by many of them as a critical time for unmistakable signs of economic improvement.

"I think autumn is when people will want to see a new mood," one senior Cabinet member said privately. "There is still no real sign of an upturn yet. It's a question of how long it will be before the country can see signs of things getting better, even just a slight improvement."

This week's Cabinet meeting and others scheduled to follow this autumn and winter were agreed to by Thatcher to give the doubters a chance to express their views on economic strategy after they complained that most economic policy decisions are made in isolation by Thatcher and her closest supporters in a Cabinet committee.

Anticipating that Thatcher's resolve would be stiffened by media touting of this week's meeting as a potential showdown with her critics, some of them said beforehand that the best they could hope for was an opportunity for their worries to be heard.

"It could be still valuable if things said there set the tone for the future work of the Cabinet," one minister said.

Despite reliable reports that many such misgivings were expressed around the table, the meeting was later depicted by Thatcher aides as a triumphant endorsement of her program. One reason for this is that her critics were unable to offer any alternative strategy.

Ther have been suggestions of increased government investment in public works to protect and create more jobs and improve Britain's deteriorating infrastructure of roads, rails and telephones. Thatcher has been forced by circumstances to approve some of this, just as she reluctantly has agreed to continue investing more money in the government-owned auto, steelmaking and coal-mining industires. But this had drawn criticism from right-wing Conservatives who want such spending sharply reduced.

Many Cabinet members also are expected to resist efforts that Thatcher and her treasury ministers warned this week would be made to significantly reduce their departments' operating expenditures in negotiations this summer and autumn for next year's budget. Most of the government's successful trimming of spending already has severely affected education, housing, local government services and some social welfare programs.

The most notable Cabinet dissenters from Thatcher's monetarist policies have been Employment Secretary James Prior, Agriculture Secretary Peter Walker and the deputy foreign secretary, Sir Ian Gilmour. A number of other Cabinet members, including the foreign secretary, Lord Carrington, and the leader of the House of Commons, Francis Pym, also are known to be skeptical.

Except for resisting spending cuts or pushing pet government programs, however, they appear unable to confront Thatcher effectively on economic policy. "No one can say to her, 'Come on now, you can't do this'," one Cabinet member said.

Dismissing periodic speculation that she might be replaced before the next election as party leader and prime minister following a Cabinet revolt, one minister pointed out that "she still has strong support in the country and party, a personal following," despite growing disapproval of her leadership in public opinion polls.