Image copyright PA Image caption Campaigners say many people have been forced to move homes, threatening their job prospects

Liberal Democrat and Labour MPs have joined forces to defeat Conservatives in a Commons vote to partly overturn housing benefit changes.

MPs backed the Affordable Homes Bill at second reading by 306 votes to 231.

Lib Dem MP Andrew George's private member's bill will now move to detailed scrutiny at the committee stage.

The issue has split the coalition, with Lib Dem and Tory MPs and ministers voting along party lines.

Since April 2013, tenants in council and social housing who are deemed to have surplus bedrooms for their needs have seen their housing benefit cut by up to 25% - a key plank in the government's efforts to reduce growth in welfare spending.

Mr George's bill would mean people who could not be found a smaller home would be exempt from the cuts, as well as disabled people who need a spare bedroom or who have adapted homes.

'Food banks'

The BBC's parliamentary correspondent Mark D'Arcy said there was now a "fighting chance" the bill would become law.

All but three Liberal Democrat MPs backed the bill. Nick Clegg, who is at the Nato summit in Wales, did not take part in the vote.

After the vote, Conservative MP Philip Davies accused the Lib Dems - who backed the benefit changes when they were initially approved by Parliament - of being "devious and untrustworthy".

He suggested there would now be a "free for all" for the remainder of the Parliament and the coalition government had "officially come to an end".

And Labour leader Ed Miliband, who has committed to scrapping the benefit cuts - dubbed the "bedroom tax" by critics - if he becomes prime minister, said it was further evidence that David Cameron's authority was dwindling.

"He is losing his MPs, he is losing votes in the House of Commons and it is Labour which is setting the agenda for fairness," he said.

Analysis by BBC Parliamentary Correspondent Mark D'Arcy

My bet is that the Affordable Housing Bill will now clear the Commons, to the sound of grinding Tory teeth - and while it might be vulnerable to death by a thousand amendments in the Lords, Labour and Lib Dem peers, plus sympathetic crossbenchers may see it through to the statute book.

Such a high-profile demonstration of Lib-Lab co-operation must chill Tory spines and show a little leg to voters lost by the Lib Dems when they joined the coalition.

Collective responsibility may have been suspended within the government today, but trust between its member parties must have been eroded.

Read Mark's full analysis.

Lib Dem Chief Secretary to the Treasury Danny Alexander said: "Today's vote was an important step in reforming spare room subsidy policy to make sure we protect the most vulnerable.

"It is absolutely right we ensure scarce housing is used as efficiently as possible and private and social sector tenants are treated fairly and equally."

'More protection'

During a four-hour debate, Mr George told MPs the most vulnerable were not sufficiently protected and he was proposing "reasonable" changes "based on the evidence" to make the policy fairer.

"We have had long enough to tell how these regulations have had an impact," the MP for St Ives - who opposed the original changes - said.

"The rules should be changed so that existing tenants are not penalised when they cannot move into smaller accommodation because this is not available in their locality."

Mr George opted to put together a bill on Affordable Homes after coming top of an annual ballot of backbenchers - which allows members to propose new legislation.

What were the original changes?

The government's changes affected housing benefit, which is paid to less well-off tenants to help with rent. In the past, claimants typically received between £50 and £100 a week.

Since April 2013, tenants deemed to have one spare room have seen their rent support cut by 14% and those with two or more rooms by 25%.

Ministers said the changes were designed to ensure social tenants get the same treatment as private tenants, whose subsidies are calculated through the local housing allowance.

Social tenants can apply for discretionary housing payments to fill any shortfall between their benefit entitlement and the rent or they can downsize.

But problems have arisen in some areas where there is a shortage of smaller homes. Campaigners say those affected face being forced to move long distances to find a property, or move into the private sector, where rents could be higher.

It means his proposed law will get more Commons time than would normally be the case for a private members bill.

Tory, Labour and Lib Dem MPs turned out in force to vote on the first stage of the bill - filling the House of Commons chamber on a day when it is normally nearly empty.

It is only the second time the coalition partners have voted against each other en masse without prior agreement since 2010 - the first was over changes to the boundaries of parliamentary constituencies.

Senior Lib Dem ministers, including Danny Alexander, Vince Cable and Steve Webb, joined Labour in the lobbies and voted against their coalition partners. It meant Mr Webb was effectively voting against his own work and pensions department.

The three Lib Dem MPs who missed the vote were Nick Clegg, Stephen Gilbert, who is on a NATO trip to Alaska, and Adrian Sanders, who was detained on constituency business.

'Big win'

Shadow defence secretary Vernon Coaker told the BBC "virtually all" Labour MPs were in Parliament in order to vote for the legislation.

Image caption Lib Dem MP Andrew George saw his bill move to the next stage

During the debate, several Tory MPs described the bill as a "Trojan horse" and said it flew in the face of the government's efforts to control the welfare bill.

"Mr George sought to lull us all into a sense of reasonableness by seeking to assert this was just a bill to tidy up and amend the spare room subsidy," Sir Tony Baldry said.

"It's quite clear from the comments of Labour that, actually, the supporters of this bill, their real intention is to remove the spare room subsidy completely."

Work and Pensions Secretary Iain Duncan Smith said it would cost the Treasury £1bn to reverse the changes and challenged critics to say what other cuts they would make to pay for it.

According to division lists published by the Press Association, a single Tory MP, Angie Bray, voted for the bill.