As many as 8,000 families in Rotherham and Barnsley have been wrongly paying up to an extra £17 a week in bedroom tax since last April.
About 400 families are eligible for a refund of as much as £700 after a government mistake led to thousands of people across the country wrongly paying the tax.
The error by the Department for Work and Pensions affects working age council and housing association tenants who have lived in the same home and been entitled to housing benefit since 1996.
When the bedroom tax legislation was drafted, the Government did not update housing benefit regulations dating from 1996.
Then, last week, the Government issued an urgent notice about the problem to housing benefit staff and said they intend to remove the exclusion.
Wentworth and Dearne MP John Healey brought up the matter in Parliament and has asked Iain Duncan Smith to establish how many people the Government thinks has been affected.
He also asked what action the Government is taking to reimburse those who have paid wrongly. The questions are due to be answered tomorrow.
Mr Healey said: “The bedroom tax is hitting disabled and vulnerable people with an average bill of £720 a year.
“It’s a callous, heartless and reckless policy that has forced families to use food banks and could end up costing more than it saves.
“The bedroom tax has always been badly thought through. Now we know the Government has levied the tax illegally in some cases.
“It’s going to be a big job for councils to put this right and put the money back in people’s pockets.”
Any of Mr Healey’s constituents who think they may be entitled to a refund can contact him for help on 01709 875 943 or email firstname.lastname@example.org