Britain is facing a year of hard truths in 2014 as more cuts are needed and the economy still has big underlying problems, George Osborne will warn on Monday.

In a grim message to start the new year, the chancellor will say the "bad news" is that there is still a long way to go before a full recovery, as he sets out a five-point plan to help the economy.

"We've got to make more cuts. That's why 2014 is the year of hard truths," he will say.

Speaking in the Midlands, Osborne will build 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 improving.

On Sunday David Cameron suggested there would be further cuts to housing benefit and refused to rule out scrapping provisions for elderly people, which include free TV licences, bus passes and winter fuel allowances.

With 16 months to go before the next election, he gave his clearest hints yet about the Conservatives' priorities for the 2015 manifesto, including more welfare cuts and higher state pensions each year for the rest of the decade.

Speaking on the BBC's Andrew Marr Show, the prime minister promised that the Tories would keep the so-called "triple lock" on pensions at least until 2020 if in power – which means increasing them annually in line with inflation, average earnings or 2.5%, whichever is highest.

He said the decision to protect the income of pensioners above others at a time of austerity was "a choice based on values, based on my values", denying it was a move to woo the grey vote.

At the same time, Cameron refused to rule out cuts to universal benefits for older people, stressing that his previous vow to keep these 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."

Cameron signalled that he wanted to cut taxes for the lowest paid before the wealthy. He did not rule out further reducing the top rate of income tax from 45% to 40%, saying such decisions had to be made on the basis of whether that would raise more revenue, but suggested it was not top of his priorities.

His remarks may be a hint that the Tories could pledge to increase the level at which workers start paying income tax above £10,000, though five million of the lowest paid earn 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 – 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."

Labour said his remarks suggested he was still "paving the way for yet another cut to the top rate of tax, a further tax giveaway for millionaires and the top Tory donors who bankroll" his party.

Michael Dugher, shadow minister for the Cabinet Office, said: "Cameron's tetchy interview underlined that he is out of touch with the country and that he has no answers to Britain's cost-of-living crisis."

Chris Leslie, shadow chief secretary to the Treasury, 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.

"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."

During the Marr interview, Cameron said a Conservative victory at the next election was achievable and he would go "all out" for it even though the party is far behind Labour in the opinion polls and a new survey suggests a third of Tory voters have deserted the party since 2010.

"We've got 16 months to the next election. This year for me is a year about governing, it's about delivering, it's about putting in place the elements of that long-term plan. I'm content that the public will judge me and the government I run and the party I run in 2015," he said.