One case was brought by “A”, a single mother whose three-bedroom council house had a panic room to protect her from her ex-partner and concerned the impact of the government’s policy on women in Sanctuary Scheme homes.

The second case, brought by Paul and Sue Rutherford, dealt with the effect of the policy on disabled children who require overnight care.

In both cases, the policy was declared discriminatory against such children and victims of domestic violence.

The Lord Chief Justice, Lord Thomas of Cwmgiedd, Lord Justice Tomlinson and Lord Justice Vos said they were allowing the appeals given as the “admitted discrimination in each case … has not been justified by the secretary of state”.

But the government will now challenge the decision after the Department of Work and Pensions (DWP) was granted permission to appeal the ruling to the Supreme Court.

In A’s case the panic room was deemed a spare room under the regulations, with A considered to be “under-occupying” her home. In the Rutherfords’ case the room was filled with things their grandson, Warren, needs each day. Warren’s genetic disorder means he is doubly incontinent, cannot walk, talk or feed himself.

The DWP said A’s case lacked credibility as discretionary housing payments were available to people facing exceptional circumstances.

In the Rutherfords case, Mr Justice Stuart-Smith said at the High Court in 2014 that such a payment made up for the rental shortfall until April 2015 and that no evidence suggested it would fail to do so thereafter.

Mr Rutherford told the BBC: “I’m a bit lost for words. I could almost cry with happiness.”

He added: “Other people are going to benefit from this decision as well. That was partly why we did it.”

A’s solicitor, Rebekah Carrier said: “These changes to housing benefit have had a catastrophic impact upon vulnerable people across the country.

“Our client’s life is at risk and she is terrified. The anxiety caused by the bedroom tax and the uncertainty about this case has been huge.

“She lives in a property which has been specially adapted by the police, at great expense, to protect her and her child.

“The prospect of having to move to another property – where she will not have any of these protections – or take in a lodger has loomed large for her during the three years it has taken this case to come to the court of appeal.”

Ms Carrier added: “She is a vulnerable single parent who has been a victim of rape and assault. She is delighted that the court of appeal has recognised the impact that the bedroom tax is having on her and others like her.

“She very much hopes that the secretary of state will now see sense and agree to change the rules to protect the small but extremely vulnerable class of women and children who need the safety of a sanctuary scheme whilst they try to rebuild their lives after surviving domestic violence.”

The Court of Appeal has granted permission to the Secretary of State to appeal to the Supreme Court against the decisions.

Responding to the Court of Appeal’s rulings, Chartered Institute of Housing deputy chief executive, Gavin Smart, said: “It’s been clear for a long time now that the bedroom tax is causing hardship and suffering for thousands of people across Great Britain.

“It is clearly a policy in urgent need of reform if not repeal. We think the government should take the latter option – the bedroom tax is not fair and it doesn’t work.”

David Bookbinder, director at Glasgow and West of Scotland Forum of Housing Associations, added: “The Court of Appeal cases highlight that the bedroom tax discriminates in a particularly acute way against specific groups. But we shouldn’t lose sight of the fact that the bedroom tax is unfairly punitive to every household it affects, not least because it was applied retrospectively to existing tenancies. It’s good to know that Scotland will abolish it as soon as it has the power to do so.”

Emily Holzhausen, director of policy and public affairs at Carers UK, gave a statement of evidence in the original case which was referenced in the judgment. Ms Holzhausen argued that families who have a clear need for additional bedrooms for a carer should be entitled to an additional room; and that alternatives suggested by the government – such as moving to smaller accommodation or taking in a lodger – are not appropriate for carers.

60,000 carers are currently affected by the bedroom tax.

Heléna Herklots, chief executive of Carers UK, said: “This policy is having a catastrophic impact on families, many of whom are already struggling practically, emotionally and financially to care for seriously-ill or disabled loved ones.

“Carers UK has argued that the policy unfairly penalises carers since it was first introduced in April 2013. Our research shows that those carers who are affected by the bedroom tax are being left unable to pay their electricity and heating bills and some families are falling behind on their rent and facing eviction.

“Following today’s ruling, we urge the government to amend the regulations to protect carers and their families. The policy is clearly having a devastating impact on vulnerable families and the Government cannot allow this to continue.”

Rebecca Hilsenrath, CEO at the Equality and Human Rights Commission, added: “Sanctuary Schemes provide an important service in placing victims of domestic violence in local authority safe houses. We are pleased that the court has found that the impact of the spare room subsidy on those housed under Sanctuary Schemes had not been properly considered, is discriminatory and is unjustified.

“Victims of serious domestic violence who are reliant on full housing benefit are in an extremely vulnerable situation and their life can be under threat. Their protection is paramount.

“The new regulations reduced housing benefits for those within the Sanctuary Scheme because their accommodation was a safe-house and therefore larger than usual. This could result in an inability to pay the rent and therefore eviction. The effect for a victim of domestic violence of losing a secure home is profound and could be extremely dangerous.”