Forty per cent of respondents to the latest YouGov poll said the Brexit deal could not be bettered by whoever would replace Mrs May if she lost a vote of no-confidence.
Conservative MPs will decide Theresa May’s fate in tonight’s vote.
However, a snap poll carried out today has revealed the British public want the incumbent to stay by a margin of 40 per cent to 34 per cent.
A total of 58 per cent of Conservative voters polled said Mrs May should stay on compared with 28 per cent who wanted her replaced.
Mrs May’s handling of Brexit also convinced 45 per cent of surveyed Leave voters she should remain in place. Only 38 per cent wanted her axed as the country’s leader.
Forty-three per cent of Remain voters also want to keep Mrs May compared to 31 per cent voting for a replacement.
Labour party voters were the only category to favour a change of leadership, with 44 per cent backing a change. A total of 30 per cent want May to continue in the post.
A total of 3,093 Britons were polled in the survey.
Of the sample, 1,068 were Conservative voters. Just 270 of the people polled were from Scotland.
Asked whether or not a different Conservative leader would be able to negotiate a better Brexit deal, the majority (57 per cent) of respondents said no.
Just 18 per cent believe a replacement, which would come from the likes of senior ministers Sajid Javid, Amber Rudd, Michael Gove, Dominic Raab or Boris Johnson, would be able to strike a better withdrawal agreement with the European Union.
No voting group said anyone else could get a better deal, including the 59 per cent of Conservative voters and 53 per cent of Leave voters who think Mrs May’s deal won’t be improved under new management.