More than a half of Liberal Democrat voters believe that Sir Menzies Campbell should be replaced as party leader as he seeks to assert his authority in face of a squeeze from Labour and the Tories.

A new Populus poll for The Times, undertaken over the weekend, highlights the decline in his personal rating after a second year of poor local election results.

Privately, senior party figures have told The Times that Sir Menzies will face criticism at the Lib Dem conference at Brighton in September unless he rallies the party.

Publicly, senior Lib Dems have made declarations of loyalty, with most signs of internal dissent confined to mutterings among grassroots activists.

According to the poll, 54 per cent of Lib Dem voters say that the party would do better to get rid of him, while just 39 per cent believe that he should stay. This means that Lib Dem voters are more hostile than the public generally, who favour his departure by a 45 to 33 per cent margin.

The party’s poll rating of 17 per cent, down three points since mid-April, is the lowest since the middle of the last Parliament. Sir Menzies’ leader rating, on a 0-10 scale, has dropped by more than a tenth since January to 4.20, by far the lowest for both him and Charles Kennedy his predecessor. Only Iain Duncan Smith, the former Conservative leader, has had a lower rating – shortly before he was forced out in autumn 2003.

Sir Menzies will try to regain the initiative and take on David Cameron and the Tories by announcing new policies on tackling poverty and extending opportunity to challenge Labour’s record, led by David Laws, his welfare spokesman, and hard-edged green policies from Chris Huhne, his environment spokesman.

Lib Dem MPs have always realised that the aftermath of this month’s mid-term elections would present Sir Menzies with his greatest moment of vulnerability, followed by another window of danger immediately after his party conference in the autumn. Beyond the autumn it would probably be too late for the Lib Dems – or any party – to change leader and establish a successor in time for the general election. However, having dispatched one leader after their brutal confrontation with Mr Kennedy 16 months ago, most Lib Dems realise that they cannot afford a showdown with his successor.

Sir Menzies, 65, has from the outset maintained his determination to lead his party into the next general election and beyond. The Lib Dems’ election results earlier this month were bad enough to put pressure on Sir Menzies, but their scale was short of the calamity that would make his departure inevitable.

Only one MP, Susan Kramer, has suggested publicly that Sir Menzies might quit if he concluded that he was not taking the party in the right direction, although she added that most MPs wanted him to stay. But “Ming must go” debates have appeared on Lib Dem supporters’ websites. One article on Liberal Democrat Voice website branded Sir Menzies as “frankly embarrassing” and “an electoral liability”. A spokeswoman for Mr Campbell said: “It’s really difficult for the leader of a third party outside an election time.” Populus interviewed a random sample of 1,504 adults aged over 18 by telephone between May 11 and 13. For more details go to www.populuslimited.com.

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