Although the ICM poll for the Guardian is generally bleak reading for Mr Major - showing the Tories at 26 per cent compared with Labour's 48 per cent - it reinforces the message that a change of leadership would not necessarily dig the Tories out of their popularity trough.
As Margaret Beckett, Labour's deputy leader, opened the party's local election campaign by saying the 5 May polls were an opportunity for electors to tell Mr Major 'what you think of him as Prime Minister', the poll underlined that Michael Heseltine remains the most popular alternative leader at present.
But the figures for those who believe that a new leader should seek a fresh mandate suggest deep public suspicion about the Tories using a change of leadership to restore their electoral fortunes. It also suggests that Mr Heseltine as a replacement would make little or no immediate difference to the party's fortunes.
This is in contrast to the summer of 1990 when the polls suggested that Lady Thatcher's replacement by Mr Heseltine would wipe out Labour's commanding lead. The poll puts the Liberal Democrats at 22 per cent.
The findings, however, do nothing to ease the Tories' painful dilemma of when to call the Eastleigh by-election, which they Conservatives seem doomed to lose. There are government divisions between those who want to have it on 9 June - the same day as the European elections and a probable total of four by-elections in Labour-held seats - and those who would rather have it at the same time as the local elections.
A June by-election in Eastleigh would prevent the Liberal Democrats using it to build an unstoppable bandwagon for the European elections.
However, it would also help to turn 9 June into a 'super Thursday' of election defeats which could amount to the worst mid-term setback for the Tories since they came to power in 1979.Reuse content