Conservative ministers vying to succeed Theresa May have sought to boost their credentials by urging the party to do more to appeal to young people.

Seven cabinet ministers widely believed to be planning leadership bids are among more than 40 MPs who have endorsed a new report calling for the Conservatives to move to the centre ground to win over younger voters.

The report, by think-tank Onward, says there are 3 million voters under the age of 35 who would consider voting Conservative if the party adopted a more moderate agenda.

It was backed by 42 Conservative MPs from the 2015 and 2017 parliamentary intakes, plus potential leadership candidates Jeremy Hunt, Sajid Javid, Michael Gove, Matt Hancock, Liz Truss, Penny Mordaunt and Dominic Raab.

The report, titled Generation Why?, found that just 16 per cent of under-35s said they would vote Conservative, although 28 per cent – around 3 million voters – said they would consider doing so if the party changed.

The study found that the Tories’ support was “dangerously” skewed towards older voters, with the age at which a voter was more likely to vote Conservative than Labour having soared from 34 before the 2017 general election to 51 today.

Onward director Will Tanner, a former aide to Mrs May, said: “Everyone is focusing on Brexit, but the growing age gap in vote intention is a bigger threat to the Conservative Party’s future.

“The only way to regain a majority is to focus on winning over a younger generation of voters – if the Conservatives do not, they risk being pushed to the sidelines, unable to govern. But there is hope, with our report showing that there are 3 million young undecided voters who would consider voting for the party.”

The study found that 83 per cent of Conservative voters were over the age of 45, with almost half (48 per cent) being older than 65.

It also found that Labour had a significant poll lead among younger voters on every policy issue. Among all voters, the Conservatives had a clear lead only on matters of defence and security, while Labour was more popular even on traditionally Tory issues such as crime, immigration and taxation.

Onward proposed a 10-point plan to win over those votes, including pledges to lower taxes, reduce the deficit, tackle inequality and control immigration. This should go hand-in-hand with a renewed focus on winning the support of female and ethnic minority voters, it said.

The proposals were endorsed by almost all of the main Conservative leadership candidates.

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Jeremy Hunt, the foreign secretary, said: “Our record in office – turning round the economy, creating 1,000 jobs a day – mean we should be the natural political home for the next generation.

“Our focus on enterprise, public services, family and home ownership are values we hold in common with younger people. It’s up to us to demonstrate our priorities are connected with the lives of young people today.”

One of his main rivals in the race to succeed Theresa May, home secretary Sajid Javid, said: “Unless we can win over younger and ethnic minority voters we cannot achieve a majority at the next election. It’s as simple as that.”

Health secretary Matt Hancock said the Tories had to work harder “to bring people with us as we work towards a positive, optimistic and outward-looking future for the UK”, while Michael Gove, the environment secretary, said: “It’s clear that young people want to see government taking action on the environment.”

Penny Morduant, the international development secretary, suggested the Onward study showed the Tories must refocus on winning over younger generations who were turning away from the centre right in unprecedented numbers – ”especially the many young women who will now not even consider voting Conservative” – while chief secretary to the Treasury Liz Truss said it showed young had a powerful sense of fairness and wanted to see barriers broken down [to give] everyone a fair shot in life.

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Dominic Raab, the former Brexit secretary, said it was absolutely crucial that Conservatives broadened the party’s appeal among young aspirational voters.

The report was published as several leadership hopefuls made fresh pitches for support.

Writing in the Sunday Times, Mr Hancock said the Conservatives needed to show the compassion and human connection that drove so many younger people. “Nobody wants to hang out with the person always pointing out the problems, rather than the one hopeful about the solutions,” he said.

Ms Truss, meanwhile, told BBC Radio 5Live she was not thinking about the leadership but was instead talking about ideas and concentrating on how the Conservative Party could reinvent itself.

Speculation about a potential pact between Amber Rudd and Boris Johnson grew when senior Brexiteer Jacob-Rees Mogg, who is reported to be backing Mr Johnson’s bid to be party leader, poured praise on the pro-EU work and pensions secretary’s “first-class capabilities” and said there would soon be a time when “we will need all the talents that are arrayed within the Tory party, not just those of Brexiteers”.