Public support for Theresa May has grown despite a disastrous party conference speech, two Cabinet resignations and Brexit talks stalling.
A YouGov poll for The Times found 34% of voters want May to stay as Prime Minister, up one point from a month ago.
Backing for Jeremy Corbyn as PM, meanwhile, fell two points to 35% and a sizeable 35% said they were not sure who they wanted to lead the country.
The Labour Party extended its overall lead to 43%, with the Tories on 40% and the Lib Dems on 6%.
The poll will be an uplifting read for Number 10 after the resignations of two Cabinet ministers in the space of a week.
Michael Fallon was forced to resign as Defence Secretary in the wake of sexual harassment allegations while former International Development Secretary Priti Patel was replaced after she was found to have held meetings with Israeli officials without telling the PM.
May’s de-facto deputy, first Secretary of State Damian Green is also facing a Cabinet Office investigation into sexual harassment allegations made against him, which he denies.
YouGov Times poll - should TMay stand down?— Mike Smithson (@MSmithsonPB) November 10, 2017
Should 32% -6
Should not 42%+3
Changes on month ago
The proportion of people who think she should stand down has also fallen. Some 32% think she should stand down now - 6 points down from a month ago, in the wake of her calamitous speech to the party conference in Birmingham - while 42% said she should stay.
The poll also showed Boris Johnson to be a deeply unpopular foreign secretary. May should sack him, said 44%, with just 26% saying she should keep him and 29% saying they did not know what she should do.
Calls for the Foreign Secretary to stand down have intensified after he incorrectly stated that Nazanin Zaghari-Ratcliffe, a British-Iranian charity worker,
Johnson also faced a torrent of criticism after making a ‘joke’ that Sirte could become the next Dubai once “the dead bodies” are removed.
On who should replace Mrs May, ‘don’t know’ topped the poll on 37%, followed by ‘none of the above’ on 27%. Of those that YouGov listed, Johnson was on 10%, followed by Jacob Rees-Mogg on 8%, David Davis and Amber Rudd, both on 4% and Philip Hammond on 3%.
The poll of 2,012 people was conducted on Tuesday and Wednesday amid a flurry of speculation about May’s future as premier.