Council house tenants are £12.5 million in arrears in Birmingham - and money set aside to help them pay their rent will run out by Christmas.

The figures were highlighted by MP Jack Dromey (Lab Erdington) as the House of Commons debated cuts to housing benefit described by critics as a bedroom tax.

Birmingham City Council received £3.7 million from the Government to subsidise tenants struggling to cope with the effects of housing benefit cuts, which target households in council or housing association properties who are considered to have a spare room.

The money, from a fund called the Discretionary Housing Payment, was topped up with another £2 million from the council’s own budget, which would normally have been spent on maintaining or improving housing stock.

But the £3.7 million is due to run out by the end of the year, the council says.

There are an estimated 13,000 households in the city affected by the policy, which the Government calls an end to the spare room subsidy. It is also known as the under-occupation penalty.

Total rent arrears have increased by a third from £8.9 million in May to £12.5 million at the end of October. The under-occupation penalty may be only part of the explanation, as some households are affected by other benefit cuts.

But while the measures were condemned by Labour MPs, Liberal Democrats and Conservatives insisted it was fair to encourage people to move out of larger properties if they did not need them - so that families in overcrowded accommodation could move in.

Speaking in a Commons debate, Mr Dromey said: “The Government gave £3.77 million to Birmingham and the council topped it up by £2 million, but there are 350 new claimants every week.

“If the current trajectory continues, the fund will run out by Christmas, and thousands of desperate people in Birmingham will face an unhappy Christmas and a bleak new year.”

But MP John Hemming (Lib Dem Yardley) insisted: “A lot of families live in overcrowded conditions. Those people come to see me and I cannot just ignore them.”

The MP also said that tenants affected by the penalty could raise cash by renting out a spare room to a lodger.

But he urged the Government to give councils more money to help them support tenants struggling to pay rent.

Conservative MP Margot James (Stourbridge) said some larger properties owned by councils and housing associations could be converted into flats.

She said: “I commend the Government for taking the tough decisions and, moreover, for their commitment to build 170,000 new social houses by 2015.

“In addition to this measure, that will help to ease overcrowding in many homes. I also hope that the Government will take a lead in encouraging housing associations and local authorities to convert some of the excess of large properties at their disposal so that we can begin to meet the needs of the 60 per cent or so of people applying for social housing for single occupancy.”

Conservative and Liberal Democrat MPs pointed out that Labour, when it was in power, had introduced similar measures for tenants in the private sector who receive housing benefit.

Speaking after the debate, Welfare Minister Lord Freud said: “It is important to remember that changes ensure housing benefit now covers households for the number of bedrooms they actually need – whether they live in the private rented sector or the social sector.”

Coun John Cotton (Lab), Birmingham’s Cabinet Member for Social Cohesion and Equalities, said: “We’re doing all we can to help the people affected here in Birmingham but, as we warned all along, the £3.77 million Discretionary Housing Payment pot was never going to be enough to meet demands.”