BARNSLEY Council will not be able to offer smaller houses to 97 per cent of the households affected by the so-called bedroom tax.
The cut - which came into effect on April 1 - means families who had one or more spare rooms will receive a reduced housing benefit payment.
But new figures released by the council show there are only 125 unoccupied one and two-bedroom properties available - enough for three per cent of the 3,664 households affected.
MP Michael Dugher criticised the government cut, saying many families already struggling could be pushed further in to debt and moved to smaller, more expensive private rented housing.
“The reality is the bedroom tax is not only unfair, it is also the wrong policy to solve the problem," he said. "How can it be right that the government has decided to cut the top rate of income tax for the richest people in the country, with 13,000 millionaires set to receive an average tax cut worth £100,000, at the same time as introducing these unfair changes?"