Ministers say they will not lift the benefits cap despite an advisory body warning it is stopping people getting help they need during the pandemic.
The Social Security Advisory Committee said people living in areas with high rental costs were losing out due to a lack of flexibility in the system.
Coronavirus meant it was “unrealistic” to expect people to find work or move to avoid breaching the cap, it said.
But Therese Coffey said they were “no plans” to review how it operated.
The work and pensions secretary said thousands of people were exempt from the cap while others were entitled to a grace period of up to nine months if they had a “sustained” record of work.
Since it was introduced in 2013, the cap limits how much any one household can receive in total benefits, including Universal Credit, Housing Benefit and Child Benefit.
At the moment, families with children and couples in London can receive a maximum of £1,916.17 a month while those living outside the capital can claim up to £1,666.67.
For single people, the amounts are lower, set at £1,284.17 and £1,116.67 respectively. The cap is designed to ensure that households claiming benefits are no better off than the average family in work but critics say it has contributed to rising homelessness and family debt.
Days before the UK went into full lockdown in March, ministers announced an increase in the value of Universal Credit and Housing Benefit and other changes to help those on low incomes unable to work due to the virus.
But campaign groups, including Shelter and the Child Poverty Action Group, have been warning for months that the more generous payments risk pushing the incomes of thousands of families’ over the monthly limit and have called for a temporary lifting of the cap for the duration of the pandemic.
Now the Social Security Advisory Committee, which advises the government on all aspects of welfare policy and recommends changes, has also called for action.
In a letter to Ms Coffey, it praised the way the benefits system had coped with a huge surge of claims in the wake of the lockdown, saying its resilience had been an “extraordinary achievement”.
But it said there were unresolved issues and many were falling foul of the cap through no fault of their own, particularly those in London where housing costs were high.
The committee, whose members include social policy experts and economists, said those affected were not in a position to take remedial action by finding paid work, which would reduce the amount of Universal Credit they are entitled to, or by moving home in order to reduce their housing benefit.
“Neither of these are realistic choices for many people at the current time,” it said.
The committee said it was concerned that the “full value” of the additional support made available in March “is not benefiting all cases because of the application of the benefit cap, particularly in areas with high rental costs”.
It recommended ministers consider measures “to ensure that the spirit and intent of the additional package of financial support it has introduced in these challenging times are fully delivered”.
But in her response, which was released on Tuesday, Ms Coffey ruled out any review of how the cap works, pointing out that those earning at least £604.59 month, on top of their Universal Credit payments, were exempt as were those who received Housing Benefit and also qualified for Working Tax Credits.
In addition, she said Universal Credit claimants who had a “sustained” work record could qualify for a nine-month “grace period” in which the cap would not apply.
“There are no plans to change the Benefit Cap,” she wrote. “There are a range of exemptions for when the cap will not be applied.
“Exemptions continue to apply for the most vulnerable claimants entitled to disability benefits and carer benefits.”
Ms Coffey said those struggling to meet rental costs could always seek help from their local authority by applying for a discretionary housing payment.
She also rejected calls from the committee for extra support for those yet to move onto Universal Credit.
The committee said it was “increasingly untenable” that those still claiming Employment and Support Allowance, Jobseeker’s Allowance and Income Support were now worse off than those on the single consolidated benefit.
But Ms Coffey said the value of these benefits had risen as a result of March’s Budget and it was “imperative that the department continues to prioritise the safety and the stability of the benefit system”.