London — Anxiety about the future is fast becoming the one thing Britain's two main political parties are experiencing in common. For the ruling Conservatives under Prime Minister Margaret Thatcher it is anxiety about the ability to hold to a policy of financial stringency when popular pressures to abandon it are mounting all the time.
For the opposition Labour Party, having just undergone a largely successful attempt by militant leftists to shunt it along the road to radicalism, the worries are more acute. They are about the party's credibility as a political movement at the next general election and beyond.
In the season when Labour and the Tories debate their policies at public conferences, Mrs. Thatcher's prospects of exploiting the disarray of her socialist foes are not as good as she may have hoped.
As the Tories assembled in Brighton for their annual conference a week after Labour congregated in Blackpool for theirs, the prime minister's personal popularity rating stood lower in the opinion polls than at any other time since she came to power 17 months ago.
More worrying to Conservative Party officials was a poll showing three-quaters of the voting public concerned about unemployment well over 2 million and increasingly inclined to blame the Thatcher government for failing to get it under control.
Labour's misfortune is that it is in a poor position to take full advantage of the public mood. The upshoot of the Blackpool conference is that the party must remain in a kind of limbo while it attempts to find a formula for choosing its leader.
At Blackpool the Labour faithful decided to change the existing system whereby the only, but failed to produce an agreed mechanism by which the selection process could be widened. That must await a special conference in January.
In the meantime the present leader, James Callaghan, has to decide whether to retire before these issues are resolved, or to soldier on. Mr. Callaghan is described by close associates as being in a dilemma. He would like to bow out, but fears that total chaos might fill the vacuum created by his departure.
This leaves the Labour rank and file with their thoughts more on internal party questions than opposing the Tories, and under normal circumstances Mrs. Thatcher would be well placed to gain from her opponents' plight.
But as they began their Brighton deliberations the Conservatives' prostations of unity were not entirely convincing.
Mrs. Thatcher and her chancellor of the Exchequer, Sir Geoffrey Howe, declared that they would not waver in their declared aim of holding down government spending and regulating the economy using monetarist methods.
But even before the conference began Mrs. Thatcher's policies came under attack from the former Conservative Prime Minister, Edward Heath, who said the government's economic strategy was wrong.
Mr. Heath, whose approach is shared by some members of the Thatcher Cabinet, believes squeezing money supply and keeping interest rates high while allowing unemployment to rise is a dangerous course.
"You cannot rely on one single means to manage the economy. You have to use other methods," he declared.
The background to the Conservative Party's debate on the economy is grim. On the average each week about 100 British firms are going bankrupt and 10,000 workers are losing their jobs, according to Labour Party supporters. In south Wales, northern England, the Midlands, and western Scotland unemployment rates are far above the national average.
The latest public opinion polls show that if there was an election now, Labour would win it with a majority of more than 100 seats.
There is, of course, little chance of an election being held. Mrs. Thatcher is not known as the "Iron Lady" for nothing, and her parliamentary majority is secure. This means that Labour at least has a breathing space while it works out its leadership problems and tries to persuade moderate supporters that last month's gains by the left wing are not a reason for splitting the party.
Perhaps the most frustrated political group in Britain under present conditions are the Liberals under their leader David Steel. With their numbers in the House of Commons reduced to 11, they remain convinced that they are rapidly picking up support in the country after their reverses in the 1979 general election.