Ed Miliband has appealed to disaffected Liberal Democrats to work with Labour against the cuts agenda being implemented by the coalition Government.

The Labour leader said Nick Clegg's decision to take his party into coalition with the Conservatives was a "tragic mistake", and declared himself ready to co-operate with Liberal Democrats "in Parliament and outside it" to oppose the direction in which the Government is taking Britain.

But his overture was dismissed by Mr Clegg's deputy Simon Hughes, one of the most influential figures on the party's left, who said Liberal Democrat supporters should "resist the blandishments of the Labour leader".

In a speech to the Fabian Society a day after Labour's by-election victory in Oldham East and Saddleworth, Mr Miliband acknowledged that the party had made "serious mistakes" in Government.

It had lost voters' trust by being too slow to admit the necessity of cuts; failing to regulate the banks; and seeming "in thrall" to the markets and remote from ordinary people's values.

"The decision of the Liberal Democrats to join a Conservative-led government was a tragic mistake, and I hope they come to see that in time," said Mr Miliband.

"Forgive me if I decline to join those who are gloating at the expense of the Liberal Democrats. Because their mistake means they are part of a Government attempting to shift politics to the right."

But he extended an olive branch to those who have opted to stay, saying: "There are many Liberal Democrats who have decided to stay and fight for the progressive soul of their party. Most of them do not want to see their progressive tradition sacrificed for personal ambition.

"I respect their choice too and I understand how painful it must be to watch what is happening to their party."

But Simon Hughes denied that Lib Dems had betrayed their values by joining forces with Tories.

"Last May, the electorate walked away from Labour and Labour walked away from government," he told the same conference in London. "Liberal Democrats took up the challenge and decided that Liberal Democrats in government would achieve far more towards a liberal Britain by joining and making more progressive the government rather than stepping back and allowing Britain to be run again by the Conservative Party on its own."