Housing charities and campaign groups have been outraged by an idea floated by Downing Street to strip housing benefits from under-25s and make them move in with "mum and dad" as a way to "make work pay" and save the UK from growing welfare expenditure.

The proposal – which was floated by No 10 earlier this week but is yet to be developed into a concrete proposal – was announced just before a speech on Thursday in which David Cameron praised recent changes to the benefits system as "the most radical, long-term reform" in the UK for a generation. A Downing Street source said: "We are always looking at ways to change the welfare system to reward hard work and make work pay."

The source said that there were many young people who are "low paid are living with their parents and can't afford to move out" and questioned if it was fair to allow unemployed young people to be able to live independently supported by housing benefits.

Currently there are just over 380,000 housing benefit claimants under 25; 57% of those have children and a proportion are in limited or low-paying work. It is is still unclear if young parents would be affected by the proposal.

Historically, under-25s have been given a significantly reduced "shared room" rate of housing benefit, as they are expected to share a flat or a house with other adults.

After an announcement in the comprehensive spending review in autumn 2010, the reduced rate has been extended to all aged under 35.

Kay Boycott, director of policy and campaigns at housing charity Shelter, warned that not all young adults had a family to fall back on. "It's outrageous that the government is considering undermining the housing safety net yet again.

"At Shelter we know that many young people simply don't have family and friends to fall back on if they lose their job, and rely on housing support to keep a roof over their head. If true, these proposals would leave thousands of vulnerable young people, many of whom may have experienced family breakdown or abuse, with nowhere else to go."

Boycott added that recent changes to housing benefit seem to conflict with the new proposal and warned of an increase in homelessness if the policy went ahead.

"Since previous changes to housing benefit will force people with spare rooms to downsize and penalise those with adult children living at home, these policies appear completely contradictory.

"Sadly it seems inevitable that we'll see an increase in homelessness as a result."

In a speech on Thursday night to launch the Conservatives' local election campaign in Wales, Cameron said, "For years people said, 'You can't reform and cut welfare – the bills are bound to get higher, this is a fact of British life and there's nothing you can do about it.'"

"We said – hang on – it can't be right that we pay people more to stay at home than go out to work. It can't be right to pay out £40, £50, £60,000 in housing benefit to families where no one works.

"We've been the first government to come in and properly get a grip on this. The Welfare Act is the most radical, long-term reform this country has seen for a generation. Making work pay, getting people trained up and back into work and ending the something-for-nothing culture once and for all."

A graduate from Bath Spa university who only wanted to be known by her first name Sarah, said that claiming housing benefits had stopped her from declaring herself homeless as living with her parents just wasn't an option.

Sarah told the Guardian that said she worked 12 hours a week in a shop for minimum wage and was supported by housing benefits to live in a shared flat whilst looking for full time work three years ago in the South West.

"Being given the chance to live separately was invaluable - it saved my life. If I had been told that receiving housing benefit was not an option, I don't know what I would have done."

Matt Griffith from campaigning group Priced Out described the policy proposal as brutal and incoherent:

"Seeking to get control of housing benefit this way is not just pretty brutal - it's fatally incoherent.

Griffith said that there was a "dysfunctional rift within government" between the Department of Work and Pensions who were in charge of the benefits bill, and the department of Communities and Local Government who "stand to one side in their remit for housing."

He added that the government was ducking long term factors in housing such as a lack of housing building.

"The proposal is targeting the least politically vocal group of recipients in an attempt to claw back savings. They will also be part of the age group that faces the worst housing offer in living memory."