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.''
Looking at the world, the Chancellor of the Exchequer, Sir Geoffrey Howe, now sees the combined gross domestic product of the US, Canada, West Germany, France , Japan, and Italy rising by 1 1/2 percent between 1982 and '83, and jumping 3 1 /2 percent in the first half of 1984.
Meanwhile, he sees consumer prices in the same six countries rising by only 5 percent this year (2 percent less than last year) and 5 1/2 percent in the first half of 1984.
In Britain, the Treasury sees inflation running at about 6 percent by the end of the year, leading Sir Geoffrey to say in his budget speech that ''the trend of rising inflation, which appeared irresistible, has been decisively broken.''
Economic growth this year is revised upward to 2 percent, and 2 1/2 percent by mid-1984. Critics say the figures are too high.
The government tried to avoid the impression that the latest budget was aimed at winning votes, even though it is expected to be the last before a new general election.
With Mrs. Thatcher still way ahead in the opinion polls, aides say she is waiting for the result of the Darlington by-election March 24 and the impact of lower oil prices before deciding when to go the polls. She could call for a vote in June or October, or possibly wait until May next year, when she will have been in office for the statutory five years.
Repeatedly Sir Geoffrey warned against ''reflation'' that would be fueled by pumping large amounts of government money into the economy to create jobs. The tax cuts he did announce Wednesday amounted to 1.5 billion ($2.28 billion), or 2.25 billion ($3.4 billion) over a full year.
For British consumers, the budget left basic tax rates unchanged, but raised personal allowances by 14 percent. It lifted a range of indirect taxes on gasoline, annual car registration, alcohol, and cigarettes. It raised child-benefit allowances and pensions, and increased the number of people beneath the income level requiring tax payments.
Critics such as the opposition Labour Party and the Trades Union Congress attacked the amount as far too small. Opposition leader Michael Foot said it was ''squalidly inadequate'' to deal with industrial decay and mass unemployment.
Government borrowing for the next financial year will be 8 billion ($12.1 billion), or 2.75 percent of gross domestic product.