President Carter's plan for fighting inflation in the United States embodies some of the drastic monetary policies that Prime Minister Margaret Thatcher has tried here in a so far unsuccessful effort to stop the accelerating deterioration of Britian's economy.

As Thatcher was forced to admit in a televised "straight talk" to the nation this week, the British economy has only gotten worse since her Conservative government began restricting the money supply with high interest rates, overhauling the tax system, cutting public spending and reducing the government's role in the economy.

The inflation rate in Britain has more than doubled to 19 percent, the highest among major Western industrialized countries. It is likely to exceed 20 percent before peaking this summer. Unemployment is rising rapidly and by next year there could be more jobless here than at any time since the Depression. Meanwhile, Britain is sliding into what forecasters say will be the worst recession since World War II.

Thatcher told Britons this week that the country's economic decline was so advanced that it would require much more time than she originally thought for her policies to reserve it. While Carter asked Americans to agree to austerity measures to fight inflation, Thatcher warned Britons they might have to endure years of much more painful austerity.

"I'm afraid some things will get worse before they get better," she said in the televised chat she used to launch a personal campaign to convince the British people to give her increasingly unpopular policies more time to work. Reminding voters "you decided it was time for change" by putting her in office last May, she told them: "Change cannot be painless."

"We did not promise you instant sunshine," Thatcher said. "We pointed out over and over again that a nation cannot accelerate downhill for years and then jam the brakes on and suddenly return to prosperity, as though the past had never happened. We had to start by slowing down before turning round and trying the long, slow climb up the hill to recovery."

While Carter is mounting his anti-inflation program in the middle of a presidential election campaign and must win congressional approval for much of his plan. Thatcher's 43-seat Conservative majority in Parliament should make her task easier. The parliamentary system's party discipline has helped her enact most of her program speedily and left most of it intact. She also should not have to face the voters again in a national election before her government's five-year term ends in 1984.

But the failure of her policies to visibly improve the economy has dangerously eroded her support in the country and inside her own Cabinet and Conservative Party. The Conservatives have fallen far behind the opposition Labor Party in opinion polls, and a nationally known Conservative candidate suffered a well-publicized embarrassment this week by winning a vacant parliamentary seat in a "safe" Conservative constituency by just 430 votes.

"There is disappointment among the people who voted for us for the first time last May," said Teddy Taylor, the Conservative who barely won the seat in the seaside city of Southend, where the Conservative share of the vote plummeted by 20 percent. "I think they expected quick results, and the grass still isn't any greener and the sky isn't bluer."

Within a month of taking office, Thatcher's government cut income taxes as an incentive to work harder and reverse Britain's steadily falling productivity rate. But to make up for the lost revenue, sales taxes were sharply increased, wiping out any gain for all but the highest income families and adding to inflation. Higher taxes on gasoline, which have helped reduce British oil consumption, also have added to inflation.

The Thatcher government has tightened the money supply by raising interest rates to a record 17 percent. But so far, this has not reduced either inflation or most wage increases, which also are averaging nearly 20 percent. Instead, economic forecasters fear the scarcity of money will force hard-pressed businesses to cut back and eliminate jobs during the deepening recession, harming rather than reviving private enterprise.

For the first time since World War II, Thatcher has eliminated all government controls on pay, prices, dividends and foreign exchange. But there are few signs of significant increases in business investment or voluntary moderation of price or pay increases. Like Carter, Thatcher believes that wage and price controls would not work even if they did not conflict with her free market philosophy.

There have already been three rounds of government spending cuts and another is expected later this month. But so far, the primary effects of the cuts have been unpopular reductions in government services, local tax increases, high charges for public housing and transportation, the elimination of tens of thousands of jobs in government-owned industries, and more hardship in the older industrial regions of northern England, Scotland, Wales and Northern Ireland.

Thatcher also has moved to narrow the wide legal rights of unions and has kept the government out of labor disputes "to allow the managers to manage." Yet a strike in the nationalized steel industry, which government officials say results from both management bungling and union stubbornness, is well into its third month.

Thatcher still believes her policies will eventually force the British to accept lower pay raises, work harder and invest more money in private businesses competitive enough to survive.

To critics who complain this is a cold, cruel approach, she promised this week that the British welfare state would continue to ensure "that those who cannot look after themselves -- the old, the sick, the children, the disabled -- are properly cared for and protected from the harsher winds of change."

But to everyone else, she lectured, "After almost any major operation, you feel worse before you convalesce. But you don't refuse the operation when you know that, without it, you won't survive. Is this perhaps beginning to get through?"