David Cameron has laid down a barrage of new ideas to cut the welfare budget, including linking benefits to wages instead of inflation, a specific £20,000-a-year cap on housing benefit and exploring if more benefits can be paid in kind rather than in cash.

The prime minister also suggested young people might not be entitled to benefits until they have paid contributions and asked whether requirements to seek work should be more intense for those who have not made lengthy contributions to the tax system.

In a vast array of proposals delivered in a speech in Kent on Monday, Cameron pointed out that in some countries claimants are required to undertake work in return for benefits within six months of becoming unemployed and said it might be necessary for those on sickness benefits to do more to improve their health.

He also suggested some single mothers with children as young as three should be required to prepare for work by writing a CV in return for income support.

In a further proposal he suggested that all such reforms, including removing access to all housing benefit for anyone aged under 25, should be considered to apply to existing claimants rather than just future claimants. Traditonally the Department of Work and Pensions implements major reforms through pilots that apply to new claimants first.

The prime minister's spokesman also said a review will look at the idea of regional benefit levels adjusted to the cost of living, although the idea was one of the few not included in the sweepingly ambitious speech. An element of regionality already exists within welfare payments.

The speech represents a shift in the Cameron's political management of the coalition, with the prime minister openly acknowledging that some of the proposals cannot be delivered in concert with the Liberal Democrats, and will have to wait for a Conservative majority government after 2015. He said he was looking ahead to the programme he plans to set out to the country at the next election.

The Lib Dem Treasury chief secretary, Danny Alexander, gently rebuffed the plans, saying the focus should be on introducing universal credit within this parliament.

Ministers have signalled that they are looking for a further £10bn in welfare cuts, mainly after the next election.

In a widely trailed excerpt from the speech, Cameron said it was "time we asked some serious questions about the signals we send out through the benefits system", arguing it had been encouraging working-age people to have children and not work when it should have been enabling working-age people to work and have children.

"If you are a single parent living outside London, if you have four children and you're renting a house on housing benefit, then you can claim almost £25,000 a year. That is more than the average take-home pay of a farm worker and nursery nurse put together. That is a fundamental difference. And it's not a marginal point."

He said that at a time of austerity, it was "right to ask whether those in the welfare system should not be faced with the same kinds of decisions that working people have to wrestle with when they have a child."

The prime minister insisted that compassion should not be measured by the size of a welfare cheque. He will also turn his fire on young people aged under 25 on housing benefit. "For literally millions, the passage to independence is several years living in their childhood bedroom as they save up to move out; while for many others, it's a trip to the council where they can get housing benefit at 18 or 19 – even if they're not actively seeking work."

Labour's Liam Byrne said the prime minister was taking the "wrong approach".

The shadow work and pensions secretary said the Labour party didn't disagree with the "basic principle" that work should be encouraged, but argued that the Conservatives' cutting of tax credits was the wrong approach for the long-term.

"We don't disagree with the basic principle that you should be better off in work. That's why Labour introduced tax credits that helped get millions back into work.

"That's why we're angry at the way they're cutting tax credits, which means that thousands of people are actually better off on benefits than in work. I think he's coming at it from the wrong approach for the long term."