Labour MPs are set to support proposed legislation that would water down the bedroom tax.

In an article for the blog website LabourList yesterday, Rachel Reeves, shadow work and pensions secretary, confirmed that her party would vote for the private members bill, tabled by Liberal Democrat MP Andrew George.

The bill, which will be voted on this Friday, would introduce exemptions to the bedroom tax for certain households.

Backing from Labour would potentially leave the Conservatives as the only remaining main party not to support the bill, as last week the Liberal Democrat leadership was set to impose a three-line whip on MPs, requiring them to attend and vote along party lines.

‘The Labour Party will support [the bill],’ Ms Reeves said. ‘This bill does not go as far as the full abolition we want to see. But we will take any opportunity to limit the terrible impact of the bedroom tax.

‘So this Friday, though most MPs will have commitments in their constituencies, I and other Labour MPs will be present in the House of Commons chamber to support the bill, so that it has the best chance of progressing through to its next stage. And in committee we will do what we can to strengthen and extend its scope.’

There are expected to be few MPs in parliament for the vote, given that the referendum on Scottish independence is due to take place within two weeks.

The Liberal Democrats might also yet downgrade to a one-line whip, which is non-binding.

A spokesman for the Department for Communities and Local Government said last week: ‘We are currently reviewing the specific contents of the private members’ bill proposed by Mr George, which has been in flux. The coalition government will collectively decide on its approach in due course.’