Fixing Britain’s youth jobs crisis will require ministers to drastically increase investment in employment support while avoiding arbitrary cuts to benefits, the head of the trade union movement has said.

Before an important official report expected next week, the general secretary of the Trades Union Congress, Paul Nowak, said the government had a “once in a generation chance” to secure young people’s futures.

In an interview with the Guardian before the highly anticipated Milburn review into young people and work, he said the costs of increasing job support, education and training would be outweighed by economic gains that would help to ease the pressure on the welfare state.

“There is no solution that is cost-free,” he said. “The government is going to have to be prepared to invest in securing the future of those young people, but also to invest to secure what is the future of our economy.

“This is where the government is going to have to be clear. Of course as a country it’s right to invest in our physical infrastructure, but also we have to invest in social infrastructure too.”

Ministers are braced for the report by Alan Milburn, the former Labour health secretary, to recommend welfare cuts to fund job support for almost a million young people who are not in education, employment or training (Neet).

The report was delayed until after the budget amid fears that the call for welfare cuts would sit uneasily alongside the tax and spending plans of the chancellor, John Healey.

Andy Burnham has said the surge in young people who are Neet is an “economic catastrophe and a moral failure” and that tougher benefits rules and more help for young people will form part of his government’s response to the Milburn report.

The prime minister has been at pains to take a cautious approach to avoid a repeat of the welfare rebellion, which forced Keir Starmer and Rachel Reeves into an embarrassing and costly U-turn on planned disability benefit cuts within a year of coming to power.

Calling on Burnham to focus on delivering a step change in employment support, Nowak said increased investment would help to bring down the benefits bill by getting more young people into work.

“We can’t afford to not do this stuff, as the benefits bill will go up if young people are not supported,” he said.

“I don’t think this government is going to repeat the mistake of the previous attempt at benefit reform, where you make arbitrary cuts, [and] where you have an impact on some of the most vulnerable people without thinking about how you support people into work.”

There is rising concern over youth worklessness. Most Britons now see the youth jobs crisis as one of the biggest problems facing the country – ranking it second only to the cost of living and above NHS waiting lists, housing, crime and immigration, according to polling by the research company Focaldata for the Jobs Foundation.

The employment charity, co-founded by the Conservative peer Matthew Elliott, is behind a national campaign to tackle worklessness that launches on Monday. It includes a pledge, backed by a group of leading employers – including Amazon, Pret a Manger, NatWest, Marks & Spencer and Shell – that have committed to support young people who have been overlooked for work.

A government spokesperson said: “We are determined to turn the tide on youth unemployment which has been years in the making.

“We have already pledged £2.5bn in youth employment support, which will deliver almost 500,000 opportunities to earn and learn, while engaging with business including some of Britain’s biggest retail and hospitality brands to create up to 200,000 jobs for young people.

“Further reform will follow the Milburn review, which will be published in the autumn.”