The Nottingham Playhouse did big business last year with Agatha Christie's ever-popular " . . . And Then There Were None," hardly the gritty social realism that made its reputation in the 1960s.

The Royal Shakespeare Company, better known for its "Hamlet" and "King Lear," has had to brush up its Shakespeare with Cole Porter's musical "Kiss Me, Kate."Such forays into lower-brow fare may horrify the purists, but Britain's government-funded theaters say they have little choice, given rising production costs and the hostility of Prime Minister Margaret Thatcher's Conservative government toward subsidizing the arts.

The new mood was set last year by Arts Minister Richard Luce when he declared: "It's time the arts world got rid of its welfare-state mentality."

The notion of taxpayers' money funding the arts has been sacrosanct since World War II. This year the state is giving $690 million to the arts, about one-third of it to theaters through the quasi-governmental Arts Council.

But some critics suggest the erosion of subsidy means an erosion of quality. They point to the RSC's embarrassment over "Carrie," its $7 million musical that flopped on Broadway after a short run at Stratford in February.

Some argue that the theater handsomely repays the government's investment. Peter Hall, artistic director of the National Theater, said last year: "It is simply daft economics, let alone daft culture, to apply a dogmatic view that subsidy is sick and bad.

"I don't believe the arts cost Britain a penny," he said. "It has not occurred to the current government that the arts is one of the few absolute success stories of Britain since the War."

The Policy Studies Institute, a non-profit research group, published a recent study showing that the arts are a $17 billion-a-year sector of the British economy, and that one-fourth of tourist income is spent on cultural activity.

It said the arts account for 2.5 percent of all spending on goods and services in Britain and directly employ 496,000 people, or 2.1 percent of the work force.

But theater insiders concede that the subsidies battle is lost and greater concessions to commercialism are inevitable.

Some even find it desirable. "It behooves us to go out and make our money from time to time and to have that commercial hard knack," Terry Hands, artistic director of the RSC and director of "Carrie," said recently in an interview with The Guardian newspaper.

The RSC faced a $1.89 million deficit last year and briefly considered closing its Stratford base. It was rescued largely by a $2.55 million grant from the Royal Insurance Company and by the commercial success of "Les Miserables," the Tony award-winning musical based on Victor Hugo's 1862 novel.

"Les Miserables," a hit here and on Broadway, is bringing the company up to $1.7 million a year in worldwide royalties.

In London, Christopher Hampton's long-running "Les Liaisons Dangereuses" has been netting the RSC $260,000 a year since it began an open-ended commercial run in October 1986.

With profits of up to $500,000 from "Kiss Me, Kate," and a $344,000 fee for the ill-fated "Carrie," even its less commercially successful ventures have brought the RSC some cash.

Still, the RSC is not alone in its new bout with commercialism.

The National Theater, the country's other major subsidized company, has been playing safe with such Broadway plays as Neil Simon's "Brighton Beach Memoirs" and Brian Clark's "The Petition," and undemanding revivals such as Arthur Wing Pinero's "The Magistrate" and George Abbott and John Cecil Holm's "Three Men on a Horse."

The National says 52 percent of its annual turnover is now self-earned.