The government suffered the first of what may be a series of heavy defeats over the welfare reform bill when peers threw out plans to dock housing benefit from people who have spare bedrooms.

Ministers had proposed that social housing tenants deemed to have one extra bedroom would lose £12 a week and people with two or more extra bedrooms £22 a week.

But peers voted by 258 to 190 to limit the penalties to only those households with two or more spare bedrooms and those with one extra room who have been offered suitable alternative accommodation.

The cost of the rebellion is put at £500m, but the government will overturn the vote when the bill returns to the Commons in the New Year.

As many as 13 Liberal Democrats rebelled and one Tory peer, the former welfare minister Lord Newton. Not a single crossbencher backed the government.

With respected figures such as Lady Hollis, the former Labour social security minister, working with crossbenchers and peers on other amendments, the government now faces the real prospect of further defeats. It has already avoided two further defeats over cuts to disability funds by one vote.

In a bid to head off Wednesday's rebellion, Lord Freud, the welfare minister, promised an additional £30m a year on discretionary housing payments to help some of those who could be hardest hit.

He said bringing in the under-occupation rules, which would be introduced from April 2013, was "essential to reduce housing benefit expenditure which, without reform, would reach £25bn in cash terms by 2014-15".

Defending the proposals, Freud told peers: "We have had to make some hard choices here in order to make the necessary savings as part of the deficit reduction plan," he said.

"The size criteria measure will only affect working-aged housing benefit claimants in the social rented sector who are underoccupying their accommodation."

He said the cuts in benefit would be 14% for people with one spare bedroom – an average of £12 a week – and 25% for people with two or more spare bedrooms – an average of £22 per week.

"In England approximately 420,000 households in the social rented sector underoccupy their accommodation by two bedrooms or more while over a quarter of a million households are overcrowded," he said.

Liberal Democrat Lord Kirkwood, a former spocial security spokesman for his party told his colleagues "If you don't vote for it you are just going to have to live with the consequences."