George Osborne has warned of another £25bn of cuts after the next election, targeting council housing for the better-off and housing benefit for under-25s.

In a grim message to start the new year, the chancellor said Britain was facing a year of hard truths in 2014 as there were more cuts to make and the economy still had big underlying problems. He said he expected the biggest chunk of the savings – around £12bn – to come from welfare in the two years after the election, as it would be an odd choice to leave this "enormous budget … untouched".

Benefits for the young and people of working age would be considered before any cuts to pensioner benefits such as free bus passes and television licences, the chancellor said.

The move forms part of Osborne's pledge to run a budget surplus by 2019 if the Conservatives are returned to power at the next election.

But Labour said the best way of reducing the welfare bill is to build more homes and get more people into employment. It also called for cuts to the winter fuel allowance benefit for wealthier pensioners.

The Treasury currently spends £1.9bn on housing benefit for 350,000 people under the age of 25 currently, of whom around half have dependent children.

Graphic: Christine Oliver

Osborne told BBC Radio 4's Today programme: "If you were going to be looking for savings in welfare, pensioner benefits is not the place that I would first turn to. I would look at housing benefit for the under-25s, when there are many people listening to this programme who can't afford to move out of their home but if you're on benefits you can get housing benefit under the age of 25. There are people, for example, on incomes of £60,000 or £70,000 living in council homes – I'd look at that."

Justifying his choice to target welfare again after around £83bn of previous cuts, the chancellor said: "When you see people on the telly who say that welfare can't be cut anymore – or, even worse, promising they will reverse the changes we've already made and increase housing benefit – ask yourself this: what public services would they would cut instead?

"What taxes they would put up in their place? Or would they borrow and spend more, and risk our country's economic stability again? This is what I mean when I say Britain has a choice."

He said he did not know when people would start to feel the effects of recovery. "There's a hard truth, which is this country is much poorer because of the economic collapse six or seven years ago, and families feel that. What is the answer? I can't wave a magic wand and make the country richer. The way the country gets richer and families get richer is by being a competitive country that attracts jobs and investment."

In a speech in the Midlands on Monday morning, Osborne said there was still a long way to go before recovery as he set out a five-point plan to help the economy. "We've got to make more cuts – £17bn this coming year, £20bn next year, and over £25bn further across the two years after. That's more than £60bn in total."

Osborne built on previous warnings about the need to intensify austerity, on top of billions of pounds of existing cuts, even though the economy appears to be turning a corner. In the speech, he said the job of fixing the economy was "not even half done". "That's why 2014 is the year of hard truths," he said.

The chancellor's negative outlook forms part of his argument that people should vote Conservative to let the party "finish the job", rather than handing control back to Labour. However, Labour said more cuts were needed after 2015 because Osborne's "failure on growth and living standards since 2010 has led to his failure to balance the books".

Ed Balls, the shadow chancellor, said the social security bill is rising under Osborne, but the best way to get it down for the long-term is to get people into work and build more homes.

"The Tories should back our compulsory jobs guarantee for young people and the long-term unemployed. And in tough times it cannot be a priority to continue paying the winter fuel allowance to the richest five per cent of pensioners," he said.

"What we need is Labour's plan to earn our way to higher living standards for all, tackle the cost-of-living crisis and get the deficit down in a fairer way."

It comes after David Cameron on Sunday suggested that more cuts to housing benefit were on the way.

With just 16 months to go before the next election, the prime minister gave his clearest hints yet about the Conservatives' priorities for the 2015 manifesto, including more welfare cuts and higher state pensions every year for the rest of the decade. Speaking on the BBC's Andrew Marr Show, Cameron promised the Conservatives would keep the so-called triple lock on pensions until at least 2020 if in power – which means increasing it annually by inflation, average earnings or 2.5%, whichever is highest.

He said this decision to protect the income of pensioners above other age groups at a time of austerity was "a choice based on values, based on my values". He denied it was a move to woo the grey vote, even though eight in 10 over-60s vote, compared with just four in 10 in the 18-24 age group.

But Cameron did not rule out cuts to universal benefits for the elderly, stressing that his previous promise to keep these handouts only extended as far as the end of this parliament in 2015. He also criticised the level of housing benefit for being "frankly far too high". "We've put a cap on housing benefit, but I still think there's more we can do to reform our benefits system," he added.

Cameron also signalled that he wanted to cut taxes for the lowest paid before taxes for the rich. He did not rule out reducing the 45p top rate of tax further to 40p, saying such decisions had to be made on the basis of whether they would raise more revenue, but suggested it was not top of his priorities. His remarks are potentially a hint that the Tories could pledge to increase the level at which workers start paying income tax above £10,000 – even though 5 million of the lowest paid earn even less than that and would see no benefit.

"I want taxes that mean the rich pay not just a fair share, as it were, in taxes, but I actually want the rich to pay more in taxes," he said. "So you ought to set tax rates that encourage people to earn, to set up businesses, to make money, and then to pay taxes. And actually what we're finding with the 45p rate is I think it's going to bring in a better percentage of money than the 50p rate is. So you should always look at how you set taxes in that way.

"But my priority if you like – the priority of this government and the Conservative party – the priority is to target tax reductions on the poorest people in our country … If I had money in the coffers I would target that money at the lowest paid."