AS he flies out to Beijing this week hoping to cheer British success at the Olympics, Gordon Brown can allow himself the tiniest of personal celebrations, according to the latest poll for The Sunday Times.

Labour’s ratings and those of the prime minister himself are getting no better, but at least they have stopped getting worse.

The YouGov poll shows David Cameron’s Tories in a 20-point lead, down narrowly from last month’s 22 points, while Labour’s support is at 25%, where it has been stuck every month since May, suggesting this may be as low as the party can go. The Conservatives have edged down from their peak of 47%, which the party enjoyed in June and July, to 45%. The Liberal Democrats are up from 16% to 18%.

Cameron’s ratings are still well ahead of Brown’s. A net 32% of voters think he is doing a good job as opposition leader, while a net 55% say Brown is doing badly as prime minister. Even on this question, however, the gap between them has narrowed slightly over the past two months.

Brown may also allow himself a small cheer for the fact that, so far at least, he is well ahead in the public mind of his main rival for the Labour leadership, David Miliband.

The foreign secretary, who has failed to quell speculation that he is plotting a challenge to Brown, is regarded by only 21% of voters as potentially a better prime minister. Brown, rated as a better leader by 38% of voters, enjoys a two-to-one lead over his rival. Among Labour supporters, Brown is ahead by 51% to 21%.

Miliband, however, appeals more to supporters of other parties. While Labour voters say they would be less likely to back the party if he was leader, Conservative and Lib Dem supporters say it would draw them more towards Labour.

A change of leader does not appear to be the answer to Labour’s problems. It makes little difference to people’s willingness to vote for the party.

With the economic news getting gloomier by the day, Cameron and George Osborne, the shadow chancellor, enjoy a two-to-one lead over Brown and Alistair Darling when people were asked whom they trusted to run the economy.

But public opinion appears to be still in a state of flux. Asked whether the Tories would be better at handling Britain’s current problems, only 33% thought they would, while 36% said they would not.

People are still very gloomy about the economic outlook and house prices, after the Bank of England’s warning last week that the economy would stagnate over the next 12 months. Surprisingly, however, they are marginally less gloomy than a month ago.

In the light of the crisis in Georgia, YouGov asked whether Britain and other western governments were caught napping by Russia’s actions. By 57% to 11% they said they were, and by 48% to 24% that the West should fear Russian military power.

People are less certain, however, of what the correct course of action should have been for the West. Only 32% think Britain and other western countries should have done more to help Georgia.

Following reports last week of a record number of Britons abroad being arrested for drunkenness, the poll tested attitudes to such behaviour. One third, 34%, said they had personally witnessed drunken behaviour by holidaying Britons. A big majority, 73%, said it made them ashamed to be British.

The poll also tested attitudes to holidaying in Britain. There have been reports of a late rush for overseas breaks, after weeks of poor weather at home. Nearly a tenth of people polled said they usually took their main holiday abroad but had switched to holidaying at home this year because of the squeeze on household finances.

A quarter of people said the bad weather had put them off holidaying in Britain in future, though 50% said they were happy to take their vacations in Britain despite the weather.

A bigger issue appears to be cost. By 40% to 13% people think that, contrary to what the British tourist industry claims, it is cheaper to holiday abroad than at home.

Full results from The Sunday Times/YouGov poll

Explore UK News

• Crime News

• Education News

• Health News

• Scotland News

Times Recommends

• Times Christmas appeal: Letter from the Editor
• Conferences — what a waste of money
• Schools supremo learns a painful lesson