The YouGov survey for the Daily Telegraph also saw his party's score drop three points to 15% while the Tories gained two to 39% and Labour went up one to 33%.

Sir Menzies was forced to shrug off reports of unrest among party members last week in the wake of a poll showing most wanted someone else to fight the next general election.

He had already helped fuel speculation by declaring repeatedly that he would not quit after conceding that disappointing election results in Scotland, Wales and England were a "mixed bag".

The new poll shows a third do not believe he is doing a good job and more than a quarter (26%) are undecided well into Sir Menzies' second year in charge after succeeding the deposed Charles Kennedy.

And when it comes to leading the country, just 6% of all voters think he would be the best option.

His spokeswoman said: "Polls go up and down; what this sort of thing shows is that people do not yet know Ming."

The poll contained some good news for Gordon Brown, who has narrowed the gap between his rating and Tory leader David Cameron's from 10 points in April to just three (41% to 38%).

YouGov polled 2,050 voters across the country between May 21 and 23.