The firmest American ally in Western Europe sees signs that an upturn is at long last on the way for the world economy. Officials close to British Prime Minister Margaret Thatcher say that as they prepare for the economic summit with the United States, Japan, and other major industrial countries in May, they are encouraged by:
* Lower OPEC oil prices, which add up to a ''lower tax on the world'' and will stimulate economic growth, even though no one yet knows how far or how fast prices will fall.
* Optimistic signs that the US economy, biggest in the world, is emerging from recession. British officials are closely studying US industrial production figures, which rose in February for the third consecutive month, and predictions the White House will revise upward its growth forecast of 3.1 percent between the fourth quarters of 1983 and 1984.
* Positive indications in Britain, where on one day, March 15, banks cut base interest rates by one-half of 1 percent (to 10 1/2 percent), manufacturing output in January was reported to have jumped 2.5 percent, the London Stock Exchange, echoing Wall Street, hit record highs, and the government brought down a modest, anti-inflationary budget.
However, government officials shadow their optimism with several caveats.
''We have had false dawns before,'' one prime ministerial adviser said Wednesday, referring in part to hopes for a British economic recovery 12 months ago.
He conceded that unemployment in Britain remained much too high. Government officials predict that it will keep rising throughout the year.
Oil prices remain a question mark. While Mrs. Thatcher welcomes a fall as a stimulus to world growth, a sharp collapse would cut North Sea oil tax revenues to the British Treasury and give the government less discretion to help industry , the consumer, and the unemployed.
Officials readily agree that British Energy Secretary Nigel Lawson faces an acute dilemma following the OPEC decision to lower its reference price to $29 a barrel.
Locked into competing for the US market wth Nigeria, Britain wants to keep its own price competitive, which means lowering it from its current suggested price to $30.50 a barrel. But undercutting Nigeria could trigger a price slide with disastrous effects on producers such as Mexico, Nigeria, and Venezuela.
''We have a vision of a renewed Britain,'' said one senior official, ''competing for world markets, with its own people spending their own money in their own ways. The budget, and the government, is consistent and prudent. We are not changing course. We are attacking inflation first, as the best way to improve the economy and reduce unemployment.''