To the tens of thousands of American tourists who have poured into Britain this summer, the country seems to be bursting with cultural largesse.

"Not since Olivier 30 years ago," is how they talk about Anthony Sher's "Richard III" at the Royal Shakespeare; Philip Glass' "Akhenaton" at the English National Opera is being hailed by the cognoscenti as superior even to the Stuttgart version; the Tate Gallery is teeming with crowds come to see the monumental retrospective of Francis Bacon; Glyndebourne, Chichester, Edinburgh . . . And every night the BBC and ITV turn out the finest television available anywhere in the world.

But just below the surface, you discover, all is not well. The arts community of Britain is filled with fear, anger and, occasionally, despair. Whether in the downstairs snack bar at Liverpool's Everyman Theatre or in the Rothschild Banking offices of the chairman of the Royal Opera at Covent Garden, the worry is that the Thatcher government's stern "monetarist" economic policies are eroding the country's postwar cultural renaissance.

"Everything that we have painstakingly built up over 30 years is being destroyed," says Peter Hall in his Southbank offices where he directs the National Theatre. In the lobby, citizens sign petitions protesting funding cuts that Hall says forced him to close down the Cottesloe, the National's experimental theater where "Glengarry Glen Ross" and Sam Shepard's "True West" first saw the light of day.

The Thatcher government is blamed for not providing an adequate level of subsidy, on which the arts have come to depend since the end of the war. It is charged that policies of retrenchment and "privatization" applied to the arts are on the way to wrecking the country's one big postwar success story.

"In the monetarist philosophy," says Hall, "you have to prove everything earns its keep and unfortunately the government believes subsidy is what you give old, ailing and no longer wanted industries. That isn't true of the arts.

"At the annual Standard theatrical Awards dinner this year, I heard Arts Minister Lord Gowrie get up and say, 'I am proud to be able to say that the West End Theatre is flourishing without a penny of subsidy.' On that very day, of the 40 shows in the West End, 19 had originated in the subsidized theater, to say nothing of the actors, writers, designers, lighting experts . . . Unfortunately we call it subsidy. If we called it investment, they might consider the whole matter differently."

The plight of the Royal Court Theatre, where John Osborne, David Storey, Tom Stoppard and Harold Pinter saw their earliest works performed, is symptomatic of the current problem. Deep cuts in its subsidy from the British Arts Council has forced the company to less than half its normal production. The Arts Council is the quasi-independent body that allocates most of the government arts funding (museums and libraries are funded directly).

Once innovative regional repertory companies are also suffering. Shakespeare, for the first time anyone remembers, was not Britain's most widely produced playwright last year; honors went instead to Willy Russell, author of "Educating Rita" with its economical cast of two. Ian McKellen, alternating in leads in the National Theatre's "Coriolanus" and "Wild Honey," feels a personal sense of loss:

"Nicol Williamson, Glenda Jackson, Derek Jacobi, Edward Petherbridge, Judi Dench -- this is where we all learned to act. The new thinking is that if something doesn't immediately make money it is either worthless, or suspect, or somehow immoral. A strange turnabout for a country that used to believe if you made money you were somehow all those things."

"Utter wreckage" is how Michael Alroyd, writing in the Times Literary Supplement described the Arts Council's decision this year to cut the total grant to literature in half.

"It is the beginning of a lobotomy that must take Britain out of the ranks of nations enjoying high culture," says John Calder, who heads a distinguished small publishing house out of his tiny office in Soho. Theodor Adorno, William Burroughs and Henry Miller are just a few of the writers Calder introduced to Britain. This year the Arts Council cut his grant by 28 percent. Next year, he's been told, he'll get nothing.

British museums were given increases for maintenance, but they had a 13 percent reduction in acquisition funds. For a country that sees its patrimony regularly bought up by wealthier museums from abroad at Christie's and Sotheby's, the reduction, to say the least, is disturbing. Museum admission fees, long resisted, are now urgently being discussed.

Today's atmosphere is far from the spirit that animated the nation after World War II when the Arts Council was born. "The arts are an integral part of civilized life," wrote Lord Arnold Goodman, an early Arts Council chairman. "A civilized government must support them. If it does not, it is falling short of its duty not only to present but to future generations as well."

Successive Labor and Conservative governments continued modestly to increase arts funding over the years. The amount remained relatively small in terms of the national budget, and always fell far behind public art subsidies on the Continent.

British subsidies rarely contributed more than a small portion of total costs, but enough money was committed to nurture fledgling groups and artists, allow for continuity and growth, and keep ticket prices low so that the average Briton could afford to attend. Result: a veritable cultural explosion.

The Old Vic, the Young Vic, Festival Hall and Covent Garden, the National Theatre and the Barbicon for the Royal Shakespeare, Peter Brook and Peter Hall, the whole cultural complex on London's Southbank, the English National Opera, the Welsh National Opera, the Scottish Opera, 15 philharmonic orchestras, chorale and jazz, poetry in the pubs, theater on the fringe, a vast network of regional repertory companies that spawned a whole generation of gifted writers, directors and actors -- all feeding into a film and television industry that made its own impact on the world.

Today, the arts community believes that the people it has always relied upon -- the minister for the arts and the chairman of the British Arts Council -- are ideologically in the enemy camp.

The government, says Arts Minister Gowrie, has reached a "plateau" in arts funding. "It's not that the party is over; it's just that the limits of hospitality have been reached."

In his offices just above Winston Churchill's wartime cabinet rooms, Arts Minister Lord Alexander Hore-Ruthven, earl of Gowrie explains:

"The reality of recent British history is that the growth of British public spending has been out of proportion with the capacity of the wealth-generating sectors to sustain." In other words, the arts ought not to expect the Treasury to cover their increasing costs.

Lord Gowrie acknowledges that the labor-intensive performing arts suffer special damage from government policies because they are extremely vulnerable to inflation. "That is very tough but it will have to be so." Lord Gowrie also says that he cannot bring himself to make an exception for the arts, tiny as they are in term of total national expenditures.

"To get into the right waters you have to give the right signals," he says. "The signals I give in respect to the arts are constant with the signals the government is giving to everything else."

He believes arts companies could alleviate many of their economic problems if they abandoned what he calls "their subsidy mentality" and made more effort "to drive for bigger box office, drive for more patronage, drive for more business sponsorship."

"I am a passionate believer in the government's philosophy," he says. "In a small way I am one of its creators; I have been an economics adviser to Mrs. Thatcher for 10 years."

Besides serving as arts minister, Lord Gowrie is the spokesman for the Thatcher Treasury in the House of Lords, roles that have brought charges of conflict of interest. "How can he be convincing pleading for the life of the arts when he is also the hangman putting on the noose?" asks Melvyn Bragg, producer of the weekly TV cultural program, the Southbank Show.

Sir William Rees-Mogg is a former editor of The Times of London. Like the BBC, the British Arts Council, which he chairs, is supposed to hold itself at "arm's length" from the government; Rees-Mogg is perceived by his critics as too close.

"I am not someone who starts out with the assumption that the government is good for the arts," says Rees-Mogg. "I start out with the assumption they are likely to be bad."

He does, however, believe the Thatcher government made a mistake in denying the Arts Council's request this year for 120 million pounds to keep pace with inflation (it received 105 million pounds). And he agrees with Lord Gowrie that the arts had better get on with the business of looking for private funding because he is quite certain that a future government less "moderate" than Thatcher's is likely to enforce truly Draconian economic measures in which "whole functions might be wiped out." Present-day dissidents, he warns, may find themselves longing for the good old Thatcher days.

Many view the idea of seeking help from the private sector with skepticism. Britain doesn't provide effective tax incentives for individual or corporate gifts. Private business sponsorship is running at under 17 million pounds annually. Says Sir Claus Moser, chairman of the Royal Opera at Covent Garden:

"The Royal Opera is just the kind of place private businesses like to support. But with all our advantages and all our efforts over many years, we are now able to raise from the private sector something in the order of between 4 and 6 percent of our costs. If we are cut again next year below inflation, Covent Garden as it exists cannot continue."

The Tate Gallery recently held a packed public debate on "What Price Arts Sponsorship?" In the end, there seemed to be a consensus that corporate sponsorship, if not accompanied by adequate subsidy, provides few answers. Too little money. Too little continuity. Too little support for the experimental -- the cutting edge, the controversial -- which are the guarantors of artistic health and a society's knowledge of itself.

"It is very hard to get private money for the innovative and the new," said John Drummond, who headed the Edinburgh Festival for years. "If the arts are alive, they are about to change. And if they work well, they are a critique of society."

Whenever the problem of British arts funding is addressed these days, inevitably the U.S. model of tax incentives comes up. Few here appear to have heard the moans and groans of U.S. artists and organizations who have complaints of their own.

Simon Jenkins, political editor of The Economist, recently came out in favor of a modified version of the American system for Britain. His proposal is for public subsidy, considerably larger than what exists in the United States, accompanied by tax incentives ("at least up to a certain limit") and pound-for-pound matching grants.

But there remains here a powerful reluctance to forgo the subsidy system that until recently has proved so successful.

"It's sheer nonsense to think the American system is the panacea," says Alan Bowness, director of the Tate Gallery. "My colleagues in the United States often envy me -- even in these straitened times. I believe in state funding. I don't think it's possible -- I don't even think it's desirable -- for the arts to be left to the private sector."

The Royal Opera's Moser agrees. He thinks that perhaps in 50 years Britain will have moved to the American model. "I hope this won't happen. Because I believe that there are things which matter so much to a nation, notably education, the arts and basic welfare, that they are part of the quality of life which it is the role of government to support."

Opinion polls and recent by-elections show the Conservatives running behind both Labor and the Liberal Alliance. With elections still more than two years away, the arts funding question has now become an important political issue. Nathan Buchan, the Labor Party's shadow arts minister, has pledged to double the government's arts budget within a year of taking office.

The really big bites, it is said, will come in 1986 when the arts will lose the grants normally provided by the Greater London Council and the six other regional metropolitan councils -- a tier of local government that the Conservatives, largely for political reasons, have voted to eliminate. To date, Lord Gowrie has committed to make up for half the loss.

Will Thatcher, as some are beginning to hope, relent? Skeptics seem to outnumber optimists. Virtually the whole British arts community is banding together in the newly formed National Campaign for the Arts to fight back on the political level.

"More people in London go to the theater than go to football matches," Peter Hall says. "So there are lots and lots of people out there who are going to say 'oy.' And we're going to mobilize them."