Theresa May has vowed to put the worries of young people at the heart of her new plan for government, after admitting that rejection by under-40s cost her a Commons majority.

Ahead of a make-or-break Conservative conference, the Prime Minister has insisted she has a strategy to deliver the promise that “the next generation should always have it better than the last”.

The pledge comes after Ms May acknowledged that voters under 40 had walked away from the Tories – rather than simply the under-25s, who traditionally preferred Labour.

At the June election, one survey suggested the Conservative crisis was even deeper, finding that voters were only more likely to back the party when they reached the age of 47.

Instead, they flocked to Jeremy Corbyn’s promises to tackle the housing crisis, abolish university tuition fees and reverse school funding cuts, Tory candidates reported back.

Now Ms May, facing the Tory faithful for the first time since the election debacle, will insist younger voters will not be neglected as she seeks to rebuild her authority.

“I understand the concerns raised, particularly by young people, during what was a disappointing election for my party,” she said in a statement.

“So my determination to act on those concerns, and crucially, to fulfil the promise of my first speech on the steps of Downing Street, is greater than ever.”

The Prime Minister added: “The social contract in our country is that the next generation should always have it better than the last. Conservatives have a plan to make that a reality.”

She did not set out any measures in the pipeline, but will be under enormous pressure to flesh out her ideas in Manchester, where the conference starts on Sunday.

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The scale of the challenge was underlined by a warning from a former Tory cabinet minister that the party is in danger of losing the support of younger voters permanently.

David Willetts said data analysed for the Resolution Foundation think tank, which he chairs, showed the lifestyles of 25- to 34-year-olds falling further behind those of older voters.

They had seen their living standards squeezed by weak wage growth and rapidly rising property prices – with pension changes likely to make it harder for them to save for their retirement.

“The worst-case scenario is we lose the support of the younger generation, and don’t regain it,” Mr Willetts told The Guardian.

In her pre-conference message, Ms May attacked Labour as “simply not fit to govern”, adding: “They don’t have the balanced economic approach our country needs and we know from last time where that leads.

“Costs rack up and working people – the very people who can least afford it – pay the price with higher taxes and fewer jobs.

“This week in Manchester you’ll see more of our plan for a country that truly works for everyone.”

However, the conference comes against the backdrop of twin Tory revolts over the troubled roll-out of the universal credit benefit and the U-turn that saw Ms May dump plans for an energy price cap.

There could also be a backlash against her admitting the Tories were unprepared for the snap election in June, even though she called it.

In the same interview, with Parliament’s magazine The House, the Prime Minister said that her party used to have to acknowledge under-25s not supporting them, but “now it’s under the age of 40”.