A few months ago, the British United Provident Association (known as BUPA), the country's largest private insurance company, opened a spiffy multimillion-dollar, 108-bed hospital here. Its color-coordinated rooms, the credit-card applications on the front counter and its catered meals contrast sharply with the drab surroundings in state hospitals.

"We believe we can offer the best of service," said the hospital's 29-year-old director, Christopher Williams, citing "higher nursing ratios, the best operating theaters, and quicker services which avoid pain and discomfort for the patients in many instances."

In a Britain worried about the fate of comprehensive, free medical care, the vision of more American-style hospitals like that one, underwritten by a major increase in private insurance, causes anguish to supporters of the troubled national health system. They fear any hints that Prime Minister Margaret Thatcher's Conservative government would establish two standards of medicine again in Britain -- the best for those who can pay, what's left for the rest.

The private health sector in Britain is still very small. Throughout the country, there are now only 150 private hospitals, with no more than 120 beds each. Doctors, including the most eminent specialists, owe their first obligation to the state service, which also has the most advanced technology in teaching and research institutions. But that could change if a politically palatable approach is found.

In early September, a secret report was sent to Thatcher and her Cabinet by the government's think tank, the Central Policy Review Staff, listing options for deep cuts in public spending, a detailed plan for dismantling much of the British welfare state.

One radical proposal considered likely to appeal to Thatcher's conservative views was to completely replace the national system of free health care with private insurance, for a saving of up to 40 percent of the country's health budget in just the first year. In addition, the report suggested charging for visits to doctors and raising the price of drugs. The needy would be provided an insurance minimum.

When the study's contents were leaked to The Economist magazine, the political and public outcry at even the idea that nationalized health care might be drastically downgraded was such that Thatcher promptly "shelved" the recommendations.

In a major speech to the annual Conservative Party conference a few days later, she felt it necessary to go even further. "Let me make one thing absolutely clear," she said. "The National Health Service is safe with us."

But there remain many people in Britain today -- including some of Thatcher's closest advisers -- who are doubtful that a comprehensive state-supported service can survive in its present form, given that it is unable to meet the increasing demands on it. "The health service is a very powerful piece of social furniture," said one senior official. He added, however, that it is becoming too expensive.

Assuming that Thatcher achieves her objective of a second term as prime minister, the role of private medicine in Britain seems bound to increase. As a first step, certain aspects of the national service could be parceled out to private enterprise to improve efficiency -- laundry, for example, or food supply. More threatening to the health system's backers would be tax relief to holders of private policies, as several Conservatives have suggested.

Over 4 million people are already in private insurance programs, mainly provided by their employers. In 1980, as worry over the future of the health service started to mount, there was a 27 percent increase in subscribers. The growth rate has fallen since, in part because the government thus far has been unable to implement any moves toward "privatization," as it is called.

With the West trapped in a prolonged economic slump, governments of all political stripes -- from Thatcher and President Reagan on the right to France's Socialist President Francois Mitterrand on the left -- are finding it ever harder to meet the costs of cradle-to-grave social benefits established after World War II. For Britain the problem is particularly severe.

Like the Reagan administration, Thatcher and the Conservative Party have scaled back wherever possible on social spending, asserting that basic assistance such as unemployment benefits for the growing number of jobless, social security and subsidized medical care would not be affected. At the same time, the government has been raising the amount of its commitment to defense.

To do all this, Thatcher's government in its 3 1/2 years in office has actually had to increase public spending from 41 percent of the gross national product to 45 percent -- an ideological paradox for the Tories similar to Reagan presiding over the biggest federal deficits in history.

For the health service alone, the percentage of gross national product has risen from 4.8 percent to 5.7 percent, according to Minister of Health Kenneth Clarke.

Harold Cairns, who has been a general practioner for 25 years in the same working-class district as his father was before him, strongly disagrees. "An increase in private care would greatly reduce the general level of treatment in the country," he said. It's "not that care wouldn't be provided. It would be just that much harder to get for the less affluent."

Ninety percent of "health contacts" in Britain are with neighborhood GPs like Cairns and these, it is widely agreed, continue to offer easily available, free treatment, reflecting the improvements in medicine of the past three decades. "Everybody has a doctor they can go to and who will come to them if necessary," he said, and in a crisis, any patient can expect a hospital place immediately.

"A man with cancer of the stomach or appendicitis will get an operation right away," Cairns explained. "It is the person with a hernia or varicose veins [who] will have to wait and wait."

It is to alleviate those delays in obtaining minor or elective operations that more people are turning to hospitals like the new BUPA one here. To a small degree, they serve the purpose of whittling down waiting lists. When Thatcher received treatment for varicose veins recently, she did so at a private clinic.

But these are only partial palliatives to a far greater problem. Health professionals, recognizing that government money will remain short for the foreseeable future, are groping for some broader solution. One compromise proposal would be to charge minimum fees for those who can afford them in existing health service facilities..

"You cannot, we believe, want to go down in history as the prime minister who won the battle for the Falklands while losing the battle for the National Health Service," The Times Health Services Supplement said in its open letter to her last month. "A civilized society is judged by the quality of its compassion for the weak and sick." They are "in greater jeopardy now," the letter declared, than "at any time" since the health service was created in 1948.