David Cameron’s plans to target benefit cuts at the young and vulnerable have come under fire from within his own party.

Sarah Wollaston, the Conservative chair of the health committee, said she did not support scrapping housing benefit for 18-to-21-year-olds, after the prime minister toured the television studios detailing some of the Tories’ proposals to cut another £12bn from the welfare budget.

In a series of interviews, Cameron repeated his pledge to lower the welfare cap from £26,000 to £23,000 per family alongside proposals to stop housing benefit for school-leavers. The cap was about a “basic issue of fairness”, he said.

“I don’t think a family should be able to get more in benefits than someone going out to work, working every day, and trying to do the right thing for them and their family,” he said.

“One of the criticisms of the cap set at £26,000, which I have heard all over the country, is that the cap was set too high. We’re responding to that.

“We’re generating these jobs. People listening to this programme don’t pay their taxes to sustain people on welfare who could work.”

He said the country was no longer willing to tolerate people living on welfare as “a lifestyle choice” and claimed Conservative plans would help “young people move into work more quickly”.

However, his proposals on scrapping housing benefit for young people came under fire from Wollaston and a number of charities.

Wollaston, the Conservative MP for Totnes, told the BBC’s Daily Politics: “That is a policy that I don’t actually support. The point is that there is a debate going forward, I would not support personally taking housing benefit from the most vulnerable. I would not personally support taking away housing benefit from the very young. I think because there is an issue here we need to discuss about intergenerational fairness ... There are many policies within parties that we have a debate about.”

Tory peer Baroness Wheatcroft later added that the Conservatives need to “get the tone right” to make sure they sound sympathetic towards those who cannot work.

“I firmly believe there is only one nasty party and it’s a very nasty party called Ukip. What the Conservative party needs to do is to be careful that it does not appear to be in the least nasty, but kind and caring and wants people to work because it is the best possible solution to them as well as the country,” she told the World at One.

The warnings came the day after academics from the LSE, Manchester and York published a new study showing the coalition’s cuts are disproportionately hitting families with young children.

Among the charities to issue warnings about the proposed benefit cap were the Child Poverty Action Group. Its chief executive, Alison Garnham, said: “Let’s be absolutely clear – the benefit cap is at least nine times more likely to affect children than adults, and the majority of adults it hits are lone parents, many of whom have children so young even the government recognises they should not be required to work.

“On the day that a major programme of research by academics from leading universities shows families with young children have been more impoverished than anyone else in recent years, we have another policy-push that would undercut the most vulnerable.”

Paul Noblet, head of public affairs at youth homelessness charity Centrepoint, weighed in on the issue of housing benefit, saying it would cause further misery for vulnerable young people.

“The 80,000 young people who find themselves homeless will think David Cameron is more focused on May’s elections than the reality that, for the most vulnerable young people in our society, housing benefit is a lifeline, not a lifestyle choice,” he said.