Theresa May must appoint a new generation of MPs to top jobs to breathe new life into the Conservative party and rescue her premiership, donors, ministers and grandees have warned.

Senior Tory figures told the Observer that while May has no long-term future as prime minister, she can secure a legacy of “restarting the party” by going ahead with a bold but risky ministerial clear-out in the next few weeks.

The plan is being widely supported by figures opposed to a Boris Johnson takeover. They believe May can deprive the foreign secretary of No 10 by staying in post for now and placing a talented pool of younger MPs in the shop window.

The prime minister is being pressed to trigger the shake-up immediately after the latest round of Brexit talks with EU leaders later this month. Downing Street said any suggestions of an imminent reshuffle were “speculation”.

Party whips have informed the prime minister’s office that there is significant support for the move. It comes in the wake of an attempt by former Tory chairman, Grant Shapps, to garner support for May’s removal. The reshuffle plan mirrors the actions of former leader Michael Howard, who used a shake-up after an election defeat to hand big jobs to George Osborne and David Cameron.

It comes as an Opinium poll for the Observer suggests the Conservatives are seen as more divided than Labour for the first time since Jeremy Corbyn’s shock Labour leadership win. Almost half (47%) think the Tories are divided, up from 40% before the conferences, while 42% think Labour is split, down from 48%.

While many mainstream Tory MPs sympathised with the circumstances of May’s calamitous conference speech, they were alarmed by the lack of ideas and energy coming from the party’s most senior figures. Others were concerned by “Labour-lite” policies on council housing and an energy price cap.

However, a major reshuffle is risky, with some fearing those sacked will help agitate for May’s early removal. Allies of Johnson are confident he will not be sacked or moved, believing his interventions on Brexit have made him impossible to shift.

One major Tory backer said that an immediate change of leadership was “the last thing” most Conservatives wanted. “If we can get some time to find a completely new candidate like we did with Cameron, that would easily be the most sensible way to restart the party,” they said. “She desperately needs a reshuffle to get some exposure to the public on who they are. The recent intakes have been quite good.”

A senior minister also said May should “be quite brutal” in her reshuffle, moving out several of the old guard including the foreign secretary. “She is in the strongest position she’ll ever be in to get rid of him,” they said.

A former cabinet minister added: “In two weeks’ time we have an important European Council meeting. Perhaps immediately after that she needs to have a proper reshuffle and promote the young bloods, bring them forward to see what they are like. It shows confidence.”

Lord Heseltine, deputy prime minister to John Major, publicly urged May to “go down fighting” and waste no time in appointing a new generation of MPs, despite the dangers.

“We have a relatively short window until the next election – I think two years,” he said. “The idea that Mrs May can lead us through Brexit and have a new leader in time for the next election is fanciful. She should create the opportunity for the party to choose not just a different singer, but a different song.

“If she took my advice, she would go for it – but she would couple it with a determination to govern and take her chance in the forum of public opinion –with an education policy that dealt with failing schools, a housing policy that built new communities and a devolution policy that empowered the whole of the country.”

Among the modernisers looking for a likely new leader there is admiration for Amber Rudd, the home secretary, but also lingering doubts about her ability to lead when she has such a precariously small majority in her Hastings and Rye seat.

Johnson and David Davis, the Brexit secretary, are seen as the most likely leaders should May go early. Some of their supporters are urging them to come to an agreement. “The best thing they could do is come to an accommodation between themselves,” said one.

Grant Shapps is gathering support for May’s removal. Photograph: A Davidson/SHM/REX/Shutterstock

While whips are confident that Shapps does not have the support of the 48 Tory MPs required to trigger a leadership contest, May’s tenure is still far from safe. She now faces delicate EU talks, a difficult budget and a cabinet clash over Britain’s future EU relationship – any of which could hasten her departure.

“To be frank, it’s nothing to do with the conference,” said one former cabinet minister. “Everyone after the election was very unhappy. The major exercise then was limping through to recess, which she did and everyone behaved well. The conference was the relaunch that wasn’t.

“Anyone can have a bad cold and have bits of lettering falling off the stage behind them, but it’s the fact that the party’s directionless. The content was extremely poor and Labour-lite. Really, she needs to consider her position.”

John Major was scathing about those agitating for a change in Tory leadership behind the scenes. Writing in the Daily Mail , he said he was “saddened to see the news dominated by those who have been driven by their own personal agenda”, adding “their conduct has undermined their own party, their own prime minister, and their own government”.

“The country has had enough of the self-absorbed and, frankly, disloyal behaviour we have witnessed over recent weeks,” he said. “It is time for the individuals concerned – both in parliament and in government – to focus their minds instead on the needs of the British people, rather than on their own personal ambition.”

Alongside his appeal for unity, Sir John called for radical action on May’s social justice agenda to “win back hearts and minds” or risk the prospect of “neo-Marxist” Jeremy Corbyn taking office.

Last night, two Conservative MEPs who voted to block progress in Britain’s Brexit talks were stripped of the party’s whip. Julie Girling, who represents South West England and Gibraltar, and Richard Ashworth, the MEP for South East England, were suspended after supporting a resolution in Strasbourg to block Brexit talks moving forward.