Controversial plans to strip young people aged 18 to 21 of housing benefit are being reconsidered by ministers amid fears in Whitehall that they would add to the homelessness bill and run contrary to Theresa May’s pledge to govern for the most needy in society.

The Observer understands that the policy, announced by David Cameron and George Osborne and due to be introduced in April, is being looked at again, as housing and homeless organisations warn it will cause grave hardship and force cash-strapped councils to meet higher costs for emergency accommodation.

Sources who have been involved in discussions with senior civil servants and ministers say the plans, which would affect an estimated 10,000 young people, are regarded as an unfortunate legacy of the austerity of the Cameron and Osborne years and will send out the wrong messages and fail to achieve their objective of saving £95m by the end of this parliament.

One source said: “The current crop of ministers and their civil servants hate the policy. It is fair to say that consideration is being given to the powerful arguments against it.”

Government officials said that the plans were still “on track” to be introduced in some form in April, although no date has been given to lay the necessary regulations before parliament.

May and her ministers – buoyant after their byelection victory in Copeland, Cumbria, where they seized the former Labour stronghold from Jeremy Corbyn’s party – are determined to continue broadening their appeal beyond Tory heartlands, not least by helping those struggling with the costs of housing and rent.

Housing and homeless organisations are now hopeful that the plans will be dropped, or at the very least that ministers will widen the list of planned exemptions for those judged as “vulnerable”, to the point where it will apply to far fewer young people.

In 2015 Cameron said the policy would “ensure young people in the benefits system face the same choices as young people who work and who may not be able to afford to leave home”.

Under the plans, which were included in the 2015 Tory manifesto, certain groups would be exempted including “vulnerable young people” and those unable to return to live at home with their parents. Those with children and those in work for six months prior to making a claim would also be exempt.

It is understood that the definition of who falls into the category of “vulnerable” could now be widened so that ministers can maintain they have honoured a manifesto commitment, while acting to nullify the more draconian effects.

Organisations including the charities Shelter, Crisis and Centrepoint have been lobbying hard against the removal of what they describe as an “essential safety net”. They argue that if young people are stripped of the ability to claim housing benefit, many who cannot or do not want to live with their parents will be driven on to the streets, leaving local authorities – particularly in London – with the huge extra costs of their obligation to provide emergency accommodation.

Anne Baxendale, Shelter’s head of policy, research and public affairs, said: “We’re deeply concerned by the imminent plan to bar 18- to 21-year-olds from receiving housing benefit at a time when rough sleeping is on the rise. Taking away the safety net that stands between some young people and the streets would be utterly indefensible.

“Put simply, not all young people have the option of living with their parents. For a small number of truly desperate young people – like those escaping an abusive household or thrown out because of their sexuality – housing benefit helps to pay for their hostel beds. Worryingly, it’s by no means clear how this group in exceptionally difficult circumstances will be protected when the new cut comes in.”

Baxendale added that the government had “failed to provide enough reassurance that the removal of housing benefit won’t perversely result in more homeless young people. Ultimately, if we don’t want to see 18- to 21-year-olds forced to sleep rough, then it’s time the government abandons these cuts.”

Seyi Obakin, chief executive of the youth homelessness charity Centrepoint, said: “Cutting this lifeline for many young people could force thousands of young people on to the streets.

“With no guarantee that exemptions to the policy for some vulnerable young people will actually prevent them slipping through the safety net, the government’s plans could cost the taxpayer more money than it saves and force more young people into homelessness.

“Rather than tie itself in knots trying to make a bad policy better the government should instead focus on the root causes of the benefits bill like rising rents and the shortage of truly affordable housing.”

A government source confirmed that discussions were under way on how wide the exemptions should be but insisted that the policy could not be abandoned altogether as it was a manifesto commitment.

Research by Heriot-Watt University found that, once the costs of vital exemptions and costs to other public services have been taken into account, the policy would save a maximum of £3.3m. It found that only an additional 140 young people would need to become homeless before the policy would end up costing more than it saved.

Opposition parties have highlighted how the number of people sleeping rough in England has risen for six years in a row with London, where property and rental costs have soared, accounting for 23% of the total. Housing charities say the policy will also mean young people having to stay longer in hostels rather than finding their own places to live.