Theresa May's political future is looking bleak after a survey revealed that a majority of Conservative Party supporters want her to quit Number 10 before the next scheduled general election in 2022.

The poll, of more than 1,200 people on the ConservativeHome website, found that 56% of respondents wanted the prime minister to resign before 2022, with 27% of Tory voters wanting May to stay on, and 15% wanting May to quit immediately. Around 1% of respondents selected "don't know".

The findings come amid the two-year-long divorce talks between the EU and the UK, and almost a month after the general election, which May called to bolster her pro-Brexit mandate only to see her majority of Conservative MPs in the House of Commons vanish.

"Despite differences and divisions with the Cabinet, and the demoralisation caused by failing to win a majority, the prime minister is set, as we write, to make it through to the summer recess, and to try to regain the initiative in the autumn," said Paul Goodman, the editor of Conservative Home.

Senior Tories and potential leadership challengers, such as Foreign Secretary Boris Johnson and Brexit Secretary David Davis, have united behind the prime minister in a bid to prevent a potentially messy Conservative leadership contest and another snap election, which could see Labour leader Jeremy Corbyn catapulted into power.

May has also faced further scrutiny because of the Grenfell Tower fire tragedy in west London. The disaster has left at least 80 dead and many more homeless.

The prime minister has launched a £5m fund to help the residents. An independent inquiry into the deadly blaze will be led by former Court of Appeal judge Sir Martin Moore-Bick. Elsewhere, May is facing a cabinet revolt over the 1% public sector pay cap, with Number 10 admitting that the public have become "weary" of the measure since its introduction in 2012.

Health Secretary Jeremy Hunt, Foreign Secretary Boris Johnson and Environment Secretary Michael Gove have called for a rethink. "I think that we should listen to the pay review bodies who govern each individual area of public sector pay," Gove told BBC One's Andrew Marr show on Sunday.

The latest opinion poll from Survation, which predicted the hung parliament result of the 8 June vote, said that the Conservatives had a one point lead over Labour (41% versus 40%). The survey, of more than 1,000 people between 28 and 30 June, also put the Liberal Democrats on 7% and Ukip and the Greens both on 2%.