The work and pensions secretary, Iain Duncan Smith, has denied claims that his controversial bedroom tax policy has descended into "total chaos" after he announced a partial U-turn to exempt foster carers and parents of teenage armed forces personnel from the charge, just three weeks before it is due to come into force.

The concessions came in a written ministerial statement after weeks of growing political pressure. The policy dominated exchanges last week at prime minister's questions in the Commons, where David Cameron defended what he called the "spare-room subsidy" from an attack by the Labour leader, Ed Miliband.

The changes will mean that about 5,000 approved foster carers will now be exempted from the bedroom tax, which from April will see people in social housing charged for empty bedrooms. They will be allowed an additional room as long as they have fostered a child or become a registered carer in the past 12 months.

Parents whose children live at home but are away on operations with the armed forces will also not be charged for their child's "spare bedroom", as long as their offspring intend to return home.

Duncan Smith said he had also issued guidance to local authorities emphasising that discretionary payments would be available to support "other priority groups" affected, including "people whose homes have had significant disability adaptations and those with long-term medical conditions that create difficulties in sharing a bedroom".

However, the opposition and campaigners pointed out that the concessions would exempt just a tiny fraction of the 660,000 people affected by the bedroom tax.

The shadow work and pensions secretary Liam Byrne said: "David Cameron's Bedroom Tax has descended into total chaos.

"Ministers have said nothing today to guarantee disabled children will be protected from his hated Bedroom Tax. They have said nothing to almost half a million households that are home to a disabled person who are set to lose over £700 at exactly the same time as millionaires receive a massive tax cut."

However, the work and pensions secretary told ITV news that he remained committed to the basic principles of the bedroom tax: "It's a very good policy, the public knows it's a good policy. This is absolutely right. All we need to do here is make sure the guidance is very clear so that local authorities can deal with those exceptional items but the main policy is absolutely straight."

The bedroom tax, due to come into effect in April, will be applied to working age claimants in social housing deemed to have more bedrooms than they require. Tenants affected will face a 14% cut in housing benefit for the first "excess" bedroom, and 25% where two or more bedrooms are "under-occupied". The government, which estimates the average household affected will lose £14 a week, says the policy will save the exchequer £500m a year.

The bedroom tax row came as the TUC published research claiming that just over half of all children will be living in below minimum income poverty standards within two years as a result of the government's welfare and tax reforms.

It said tax and welfare changes, including tax credit cuts, and the VAT rise to 20% would be compounded by wage freezes in the public sector, pushing 500,000 more children into poverty.

TUC general secretary Frances O'Grady said: "By the 2015 election, the majority of children in Britain will be living below the breadline. For any civilised society, that should be shaming."

A spokesperson for the Department for Work and Pensions (DWP) said the bedroom tax concessions represented a "clarification" rather than a u-turn. "It was always our intention that foster carers and armed forces personnel would be covered by discretionary housing payments (DHPs) and therefore not affected. We will now adjust the regulations to give greater certainty."

David Orr, chief executive of the National Housing Federation, which represents housing associations, said: "The DWPs' continued claim that DHPs [additional funding to mitigate the worst effects] will protect all of the most vulnerable is simply not true. Even if DHP was divided equally only among those receiving disability living allowance, they would receive only £2.51 a week, compared to an average loss of £14 per week. It doesn't add up."

Robert Tapsfield, chief executive of the Fostering Network, which has been lobbying for the change, said: "This change of policy means that foster carers can sleep easy knowing that they will not be punished for providing homes for some of the UKs most vulnerable children."

Heléna Herklots, chief executive of Carers UK, said: "Government must now act to exempt carers who cannot share with disabled partners, disabled children who cannot share with siblings, and families who need space for medical equipment or home adaptations. These families should not be forced to appeal to a limited pot of discretionary funding – they must be exempt from the changes."

Chartered Institute of Housing chief executive Grainia Long said: "These concessions are welcome but they are not enough. Other people are also unfairly affected, for instance, people who need a bigger home because of a disability should also be exempt.

"We know that the open market doesn't cater particularly well for these people, and they should not be penalised for living in social housing when in many cases there is nowhere else for them to go."