London — If you cross Waterloo Bridge from the Strand these rainy spring evenings in London, your eye is caught by flashing electric words marching over a giant screen on the far bank of the Thames.
The words cut through rain and gloom to announce the plays showing that evening in a building that shines at night like a ship at sea - the enormous, government-subsidized, concrete and glass National Theatre.
After running through tonight's program, the newly installed electronic wizardry shouts that seats are available at low prices - and the lights turn into a string of cartoon theatergoers, jumping up and down for joy.
Does joy, however, extend throughout the world-renowned London theater? Yes . . . and no.
Acting and putting on plays are among the things the British still do best. London in particular is a pinnacle of excellence, and a magnet to hundreds of thousands of tourists every year.
But a long look backstage at the National, the Royal Shakespeare Company (RSC), and the commercial West End theaters (a term that covers all commercial theater in the London area, not just in the physical region known as the ''West End'') shows an increasingly serious financial strain, especially within the commercial theaters.
Attendance averages about 60 percent per show. Among the reasons:
* A dramatic rise in rented video recorders and cassettes in British living rooms.
* British tax laws that discourage private patronage.
* The deep economic recession, which has drained money from the economy, cut back government budgets, and caused families to think again before going out to anything but a smash hit.
''The recession has definitely had an effect on audiences,'' says RSC general manager David Brierley from his office in Stratford-on-Avon. ''People don't want to pay more, but we keep pushing up our top prices to stay afloat.''
''Obviously there's pressure at the margins,'' says National Theatre general administrator Michael Elliott in one of the lobbies of the National Theatre that overlooks a sweep of the Thames from St. Paul's Cathedral to the Strand. ''You have to put on something special all the time, such as our production of 'Guys and Dolls.' ''
The new electronic sign aimed across the river is just one of many efforts the National is making to attract customers - and balance its books.
In addition, the West End says, there is the competition posed by government-subsidized companies such as the National Theatre and the Royal Shakespeare.
While the Society of West End Theater praises both as success stories, spokesmen such as development officer Vincent Burke also say that subsidies allow the National to put on plays that the commercial theaters might otherwise have used, and to purchase the rights to scripts that it then stockpiles for its large repertory company. The National includes three separate theaters, and the Royal Shakespeare runs four.
Competition also comes from television, which pays well and has an insatiable appetite for scripts.
Says Mr. Burke, ''The commercial theater is finding it more and more difficult to find suitable products to put on its stages.''
It would be wrong to start preparing an obituary for British theater marquees. They are still bright - 45 of them in London alone - and they have survived countless rumors of demise over the years.
West End commercial theaters alone sold 9 million tickets last year, 5 percent more than the year before. They raked in $:59 million ($88.5 million) at the box office.
This year theatergoers were flocking to see the big hits even in the usually slack pre-Easter season: the US production of ''Pirates of Penzance,'' the musical ''Cats,'' ballet star Wayne Sleep in ''Dash,'' ''Song and Dance,'' and Tom Stoppard's ''The Real Thing.''
Yet directors, managers, and planners are extremely concerned about the future. In interviews, they said they could see only one long-term solution - devising methods to siphon off more support from the government treasury.
After gulping down a quick lunch at one of his own theater buffets, and before racing downstairs again for more rehearsals of a new musical with score by Broadway's Marvin Hamlisch (''Chorus Line'' and ''They're Playing Our Song'') , the bearded and incisive Sir Peter predicted:
''In 10 or 20 years most of the theaters in London will have disappeared . . . unless they are subsidized in some fashion.
''Theater is handmade, and very expensive,'' he continued. ''In the 19th century, wages were low and labor available. Today each theatrical performance is like a handmade piece of furniture, fashioned just for you, every night. . . . Without subsidy, the West End will fail.''
One Peter Hall solution is for government and theater to devise a fund which helps new productions and into which profits are plowed back.
Across the bridge in his Covent Garden office, Vincent Burke nods in agreement.
His job in the Society of West End Theater is to keep commercial theater alive in an era of recession and television. Among a number of other innovations: the successful half-price ticket booth in Leicester Square.
''Sir Peter is right about the need for government subsidy,'' he says, ''though I don't use the word subsidy, because it has the meaning of a handout.
''I prefer talking about a government investment. About 30,000 people come into London every night to see live theater - 20,000 of them eat out. About half use public transport. Two out of every 3 overseas tourists give the theater as one reason for coming here in the first place.
''When theaters do go dark between shows, local pub and restaurant owners say their business drops by 40 to 50 percent.''
As Mr. Burke points out, a fund of the kind Sir Peter described already exists. It is the Theatre Investment Fund (TIF), started with a one-time government contribution in 1976. But the fund has fallen on hard times, and the Society of West End Theater is lobbying hard for the government to pump more funds into it.
''The TIF has been putting $:5,000 ($7,500) into new performances, as seed money that allows producers to approach other potential investors,'' said Mr. Burke. ''We'd like to see the fund built up to $:125,000 to $:150,000 ($187,000 to $225,000) with government help.
''It is crucial for the fund to be restored. . . . The West End theater doesn't have any problem with the big hit musicals, or with any play starring Glenda Jackson, for instance. It's the marginal plays that are of concern.
''Overheads here are very large. Many London theaters are old and not flexible - though I should point out that none have closed and seven have opened since 1970, including the Apollo Victoria, a former cinema.''
Since 1970, the number of seats available in West End theaters has risen by 25 percent, to between 50,000 and 55,000 per night.
Taking Mr. Burke's figure of between 30,000 and 35,000 seats being filled each time, average attendance is about 60 percent, considerably too low for comfort.
The Society of West End Theater has been redoubling its efforts to offer group and old-age discounts, half-price tickets on the day of performance, and other incentives.
It also hopes the striking drop in the value of the pound against the dollar will encourage more Americans to come here this year: It takes $18 to buy a top theater ticket today, compared with $28.80 two years ago.
Next: Even inside Britain's subsidized theaters, life can be hard.