Sir Vince Cable, pictured on the election campaign trail in London in May, said he has been 'sounded out' by remain-backing Tories

Lib Dem leadership front-runner Vince Cable has said he is in secret talks with Tory MPs to water down Brexit.

The former business secretary said he is speaking to Remain-backing MPs about cooperating in parliament.

The claim came as the Lib Dems tabled an amendment to the Queen's Speech that would keep Britain in the single market - a move that has been ruled out by the government and Labour.

Theresa May has been scrambling to tie up a deal with the DUP to prop her up in power after the bombshell election result stripped her of her Commons majority.

Even with the support of the Northern Ireland party's 10 MPs, only seven Tories would need to rebel during a vote in the House to defeat the Government.

This wafer-thin working majority means the PM is at the mercy of her MPs, and a backbench Tory rebellion could plunge her Brexit plans into crisis.

Sir Vince said remain-backing Tories are starting to organise behind the scenes and have been tapping him up to discuss mounting a parliamentary assault on the government's Brexit plans.

He told The Telegraph: 'Informally all kinds of networks are being established and I have been sounded out by several of them.'

And Sir Vince said the 'tribal differences between the parties have broken down' and that instead he wants MPs from all parties 'to be encouraged to work together'.

He said: 'There are a lot of Conservative MPs who may not have put up a flag called Remain but are very, very worried about the more extreme options on the table and would like to keep either the customs union or the single market or both.'

Sir Vince praised Tory arch europhile Ken Clarke, and said: 'We have to work with like-minded people across the spectrum trying to get a softer, more sensible version of Brexit.'

His comments suggest that an alliance of remain-backing MPs from all political parties could launch a guerrilla warfare in the House of Commons to keep many of the tenets of membership.

The move would enrage voters who backed Brexit last year and do not want their MPs to overturn their referendum votes in the Commons Chamber.

Mrs May this week unveiled plans for eight Brexit bills which will deliver on the historic vote to leave the EU and bring tackle sky-high immigration.

Theresa May, pictured in Brussels today, where she made a 'fair and generous' offer to allow the 3.2 million EU nationals living in the UK to stay after Brexit

But with her majority wiped out, she is bracing herself for some difficult clashes in parliament which could imperil her plans.

The Liberal Democrats want Britain to stay in the single market - which would effectively mean the UK would have to keep its borders open.

While dozens of Labour politicians have publicly backed plans to stay in the single market - despite their leadership's position.

And if Tories join the throng, the PM will face a tough fight to push her plans through.

David Jones, the former Brexit minister who lost his job in last week's Cabinet reshuffle, admitted that 'the arithmetic is challenging but I think deliverable' in the Commons.

And he said the Brexit-backing Tory MPs will fight back by striking alliances with their Labour counterparts like Kate Hoey.

He told the newspaper: 'MPs from all sides should now be working to ensure a smooth and successful Brexit.

'Voters will not forgive politicians who are indulging in shabby games rather than supporting the Government in delivering on the referendum result.'

The secret talks have emerged as Mrs May is in Brussels where she has made a bold offer to allow the 3.2 million EU nationals living in the UK to stay after Brexit.

But she received a chilly response from Brussels, with European Council president Donald Tusk complaining that the proposals were 'below our expectations'.