David Cameron is enjoying the highest Tory rating for 13 years

The ICM poll for The Guardian newspaper suggests the Tories have pulled ahead on some of the issues where they trailed Labour at the last election.

The poll puts the party on 38%, its highest rating for 13 years, with Labour on 34% and the Lib Dems on 20%.

It also suggests Labour's support would fall if Gordon Brown was leader.

Asked how they might vote in an election with Mr Brown, the man widely expected to be the next Labour leader, pitted against Tory leader David Cameron and Lib Dem leader Sir Menzies Campbell, 40% backed the Conservatives, 31% Labour and 19% the Lib Dems.

But 46% of those surveyed thought Mr Brown was more trustworthy than Mr Blair, whom 26% said they trusted more.

Mr Blair had a narrow lead over the chancellor in who was seen as having the wider appeal - and that lead was extended when only Labour voters were polled.

Public service ratings

ICM interviewed a random sample of 1,001 adults by telephone between 19 May and 21 May. The results were weighted to reflect the population.

The Tories' overall rating is their highest in an ICM poll since 2002, during the fuel protests.

They were seen as the best party with the best policy on health by 26% of those questioned, compared to 24% for Labour and 13% for the Lib Dems.

And on education, the Tories led by 30% to 28% for Labour and 13% for the Lib Dems.

They also lead Labour by 12% as the party with the best law and order policies and are also clearly ahead on asylum and immigration in the wake of the foreign prisoners crisis.

But Labour is still ahead when it comes to handling the economy, leading by 37% to 30% for the Tories and 9% for the Lib Dems.

And Tony Blair may also be reassured that Labour's standing has risen by 2% on last month, when ICM suggested the party's support had fallen to the lowest point since the 1987 general election.