London — Britain has been wrestling for a decade with what a senior Cabinet minister now calls its second industrial revolution - one that requires fewer and fewer workers to run the economy, new ideas to compete abroad, and solutions for the mounting number with no jobs at all.
The economic picture here has seemed so bleak for so long that any positive signs of upturn or improvement must be greeted with caution. The Conservative government itself gloomily admits that those out of work will keep rising above the current 3 million mark for at least the rest of this year.
Yet, deep within the stresses and strains of a country being forced to realign its industries, the structure of its work force, and relations between bosses and workers, some signs of hope have begun to glimmer.
Two immediate factors prevent officials turning cartwheels of joy.
One is that suddenly rising US interest rates is causing genuine alarm here that the pound sterling will lose even more ground abroad, British interest rates will be forced up to compete with American ones, and British hopes will be nipped by an American fiscal frost.
As soon as the first US banks announced prime interest rate raises Feb. 1, the governor of the Bank of England, Gordon Richardson, joined the public chorus of government voices in Western Europe calling for President Reagan to bring his rates back down. Europe complained at the Ottawa summit last summer.
The second factor curbing optimism here is a mixture of economics and politics. Three million people out of work means 3 million sets of families and relatives also living with the daily impact of joblessness: 12 million individuals or more. These people, plus opposition political parties, are likely to dismiss as campaign rhetoric any extravagant government claims between now and the next general election in about two years.
Daily headlines here tell of the railroad drivers' strike, of rumbling trade union opposition to the government's new industrial relations legislation just introduced in Parliament, and of growing alarm at American interest rates.
Yet, economists see signs that the government's strict monetarist policies over the past year have begun to have some effect.
The respected Economist, a London weekly, says last year's budget ''saved the economy from capsizing.'' Prime Minister Margaret Thatcher herself is apparently ready to loose the purse-strings slightly on March 9 by easing some tax burdens. Her right-wing critics, including captains of industry and some senior figures in her own party, are not satisfied, but the latest economic figures are causing considerable comment.
In the last decade, the amount of money circulating in Britain has risen 20 times faster than output, so officials are heartened to see manufacturing productivity jump between 7 to 9 percent last year. Wages are being held down as workers realize any job is better than no job: in the private sector they are rising only between 4 to 6 percent, and in the public sector, prospects of a widespread series of strikes have receded with the recent settlement of the miners' strike.
The railroad drivers remain a problem, but the economic impact of likely settlements is already known. Workers are, in fact, striking less: days lost to strikes is lower now than for 15 years.
Britain is again earning more abroad than it is buying from abroad: in fact, last year's trade surplus could be a record (STR)6 billion ($11 billion), officials estimate, and double the surplus of 1980. December was up strongly, as North Sea oil revenues improved, and imports fell almost 10 percent.
The overall rate of inflation has dropped from 18 percent in 1980 to 12 percent today.
Signs now are that the Chancellor of the Exchequer (treasurer) Sir Geoffrey Howe, is prepared to allow between (STR)1 billion and (STR)1.5 billion (between
This would be criticized sharply by trade unions, and by Labour, Social Democratic, and Liberal parties as far too little. British industry wants around (STR)3 billion pumped into the economy, including a reduction of the payroll tax (called here the ''national insurance surcharge'').
But the prime minister and the chancellor would point to a modestly encouraging budget as a sign of success - and would hope privately that it would help them politically with the electorate as well. The Social Democrats continue to score around 35 percent of the vote in local by-elections, often taking Tory votes.
No one here believes the long recession is about to end, or that Britain has weathered successfully the blows of oil price jumps (1973, 1979), over-manning, wage raises unmatched by productivity in the last two decades, and a tragic slowness to shift from outmoded industries to the microchips, synthetics, and service industries of the future.
The senior Cabinet minister who runs the House of Commons for the prime minister, Francis Pym went out of his way Feb. 1 to warn publicly that ''public expectations are too high.'' Economic recovery, he argued could only be long-range. The optimistic, carefree days of the 1960s had gone. Living standards could not increase, nor unemployment fall, in the short-term.
Mr. Pym said the first industrial revolution demanded vast new manpower in Britain. The second one, occurring today with much travail, meant vastly more efficient machines, fewer workers, and imaginative solutions for those out of work.