London — The cash registers are ringing hard in shops across Britain. . . . A friend in north London is being told the rush for home mortgages is so great this spring that he might have to wait four months to buy a house. House prices are kicking upward for the first time in months.
Sterling is growing stronger abroad. Inflation is lower than it has been for 13 years. Oil prices are down.
Could it be? Could the British economy, so hard hit for so long, finally be pulling out of its decline?
All that can be said for certain is that the signs are promising. But manufacturing is still weak, traditional industries such as steel and textiles are still weak. It is still much too early to tell.
Britain can't regain its financial health on its own. The United States is the economic engine of the Western world. Unless its interest rates go down and its output goes up, Britain and all of Western Europe must wait for better times. The point is emphasized by politicians from all parties and by economists as well.
Most now agree that the signs for recovery seem more interesting than in previous years, even though all warn against ''false dawns.''
Factories have been producing more in the US, where industrial output has been rising, and now the same trend has appeared in the European Community (EC). Preliminary figures just out in Brussels show industrial output still in the red in 1982 - but down by only 1.6 percent, compared to 2.2 percent in 1981.
In Britain, spending in shops rose by 4.5 percent in March compared to a year earlier. Beneath the surface, the signs are good that spending will continue: Bank interest rates have just fallen again, mortgage rates are staying low, and tax reductions in the recent budget indicate that disposable (after-tax) income will rise.
Last year British families found their disposable income down by 1 percent, but figures show they spent anyway, either by dipping into savings or by borrowing.
Inflation is still less than 5 percent in Britain, and 5.7 percent (in February) across the EC. But not all the signs are rosy. Unemployment is more than 3 million and rising in Britain, and 10.5 percent (11.5 million) in the EC as a whole.
One question now: In countries like Britain, will all that extra money going into the shops be spent on locally made goods (adding to the recovery) or on imports (holding it back)?
Meanwhile, London is about to see a new extension to its famed Tate Gallery on the Thames. Attached to the Tate facade, it will be called the Clore Gallery. Its foundation stone has just been laid by the Queen Mother, and its purpose is to house the Tate's collection of J. M. Turner paintings.
Attracting much publicity is the controversial architect, James Stirling. Architect Philip Johnson in the US has called him ''the world's greatest living architect'' while others have criticized the monumentalism of his recent work. He has carried out commissions in Italy, West Germany, and the US, but the Tate extension is his first building here since 1976.
Drawings now on show indicate that each facade is treated in a different way - the main facade in classic style, a wing faced in brick, and what London Times critic Deyan Sudjic calls a ''modern service entrance, free of historical mannerisms.''
Writes Sudjic: ''The whole building is difficult not to say prickly. . . . Not unlike Stirling himself. It demonstrates the importance in fact of the individual over the conventions of style in the most potent fashion.''
Back among the politicians, the big question is whether brighter economic lights mean Prime Minister Margaret Thatcher will go to the polls in June - or will she wait until October, or even until the last possible moment, next May, when she will have been in office for five years?
She may wait, if only because the opposition parties would prefer to fight her now. The Reagan administration believes (as do most observers here) that she will win any poll, thereby keeping Britain a staunch American ally.
The Labour Party says that, if elected, it would order US bases out of Britain within five years, as well as reject cruise missiles and the Trident submarine missile system.
While many here doubt that a Labour government would actually do all that, uncertainty would affect the NATO alliance. US officials warn that US investment and corporate headquarters abroad might begin to leave London.
Mrs. Thatcher is inclined to wait as long as possible, but some Cabinet heavyweights, such as Chancellor of the Exchequer Sir Geoffrey Howe, are said to be urging her to call an election sooner rather than later, before inflation and unemployment look worse. She is determined to wait until after local elections May 5, however, and all the election-date speculation about June may yet turn out to be wrong.
Those pushing her to go soon say she should strike while the public opinion-poll iron is hot: with the Tories out ahead with 43 percent of the vote; Labour up from 27 to 34 percent; and the Social Democratic-Liberal alliance slumped to 22 percent. A Gallup poll puts the Tories at 40.5 percent, Labour at 35 percent, and the alliance at 22.5 percent.