The YouTube video artist Cassetteboy made his anti-Brexit stance clear last week when he mocked the prime minister with the words: “It is wrong to believe the fable that Theresa May belongs at the negotiating table.”

It is a sentiment echoed by millions of voters, many of them newly registered millennials, who used the general election to demand many things from MPs, including a softer Brexit than the one planned by May.

Cassetteboy’s video was viewed almost one million times in the two days before the election. It’s not the first time his cut-up edits of prime ministerial speeches have proved a hit, but this time it seemed to resonate with 18- to 25-year-olds just as they were signing up in droves to vote.

Rob Wilson, the ousted Tory MP for Reading East, who accused No 10 of running a disastrous campaign, said that the university students who populate his side of the city played a large part in the 16% jump in Labour’s local vote.

May’s response has been to accuse Labour of pork-barrel politics. Her lieutenant Amber Rudd accused Jeremy Corbyn of buying votes with promises to the young of free university education, higher spending on schools and better mental health service provision – something college-age students make increasing use of.

But to accuse Labour of bribing its way to electoral success is to miss an important point about the young. It is undoubtedly true that a simple and popular policy like tuition fees will get the attention of young people.

How could they not notice an offer to wipe out £40,000 to £50,000 of loans, and with it the possibility of paying more than £400,000 in extra tax by the time they are 50 years old to pay them back?

But the criticism of sky-high student fees is not so much around the principle of students paying something towards their education. The focus of student anger was directed at the astronomical size of loans under the new scheme and the barely understandable tax system used to claw them back. Then there was the likelihood that the next generation would be saddled with billions of pounds of unpaid debts.

It is all of a piece with the Cameron/Osborne policy legacy, inherited by May, that manufactures ways to kick debts down the road while professing to tackle them here and now.

It has taken time for the implications here to sink in, despite plenty of warnings about the rocketing levels of student debt in the US, where student loans have become the second highest consumer debt category – behind only mortgage debt – at $1.3tn.

Young people have seen the dream of home ownership pushed out of reach. Photograph: Steve Parsons/PA

Unhappiness with student fees chimes with the concerns that young people have over the Tories’ plan to quit the European Union and cut the UK off from the continent, while cutting taxes on business and imposing steep cuts to public services.

As Torsten Bell, director of the Resolution Foundation, wrote following the vote, a bleak vision of young people’s future was brought into sharp focus by the election campaign.

“In the past two decades, young people have seen the dream of home ownership pushed further out of reach – the number of young families owning their own home has halved since the 1990s in places as far-flung as Bristol, Manchester and Leeds. This is not just a London problem,” he said.

“Young people experienced the tightest pay squeeze in the wake of the financial crisis – with real pay falling by 13%. A decade on, they are still moving jobs less frequently than they used to, and those born in the late 1980s are the first cohort in living memory to earn less than the one born 15 years before them,” he added.

It seems obvious that millennials, even just taking an impressionistic view of the party’s manifestos, would consider Labour to be “on their side”. The shock was that so many of them were among the two million people who registered to vote before the poll and went into the polling booths to mark their preference. But the young must stay vigilant: another lesson of the campaign was that there are vast numbers of older voters who still demand that the government fund their retirements with universal benefits.

It was a disaster for May when the Tory manifesto threatened a tax on social care that became the “dementia tax” and a vague commitment to means-test the winter fuel allowance. Wilson says it was the spark that ignited the Labour campaign.

Corbyn’s answer was to give pensioners everything they wanted, too. He promised to maintain the triple lock and winter fuel allowance for all pensioners, and freeze the pension age at 66.

But a high financial safety net for pensioners will prove to be hugely costly without some deep thinking about the state’s responsibility to fund health, housing and social care for this group.

Caring for the old is one of the biggest drags on growth across the developed world. Labour promises to deal with the problem out of general taxation. Unfortunately, that won’t leave much money for the young. There are choices to be made.