Theresa May has been told that offering a softer Brexit would cause her party to “explode” as deep divisions among her cabinet were played out in public.

Former Tory minister Philip Lee warned that attempts to compromise over a customs union would enrage Brexiteers, after cabinet ministers clashed openly over whether Ms May should ditch one of her key red lines.

The prime minister has sought meetings with opposition parties to break the Brexit deadlock, after the Commons overwhelmingly rejected her deal by a record 230 votes on Tuesday.

But Labour leader Jeremy Corbyn has refused to attend talks unless Ms May takes the threat of a no-deal exit off the table and opens discussions on the prospect of a customs union - something No10 regards as incompatible with delivering on Brexit.

It comes after fresh splits emerged in the cabinet as senior ministers David Gauke and Amber Rudd both refused to rule out a customs union with Brussels, with Ms Rudd saying "nothing should be off the table".

Dr Lee, who resigned from government over Ms May's Brexit deal, said a softer Brexit could prove more divisive among Tory MPs than the original referendum result.

Asked whether a customs union could be part of a compromise, Dr Lee said: “The idea they can entertain a customs union, a full customs union, and the European Research Group (ERG) are going to explode. I can’t see it myself.

"And I think actually if they go down the path of reaching out this is the major problem with the Norway option.

“If people are talking about party splits, I think that has the potential to split the party much more than this [referendum].”

Shadow international trade secretary Barry Gardiner echoed his comments, saying Ms May was sticking to her "red lines" because any compromise would "break the Conservative Party".

"She knows the only way to get a deal through parliament is to break some of her red lines, but she knows that if she changes her red lines she breaks the Conservative Party," he told BBC One's Breakfast.

"She knows the ERG will desert her. That's the dilemma she's in."

It comes after Mr Gauke, the justice secretary, said that Ms May must not be “boxed in” by red lines, adding: “We need to be prepared to be flexible.”

Police separate clashing Brexit protesters outside Parliament Show all 11 1 /11 Police separate clashing Brexit protesters outside Parliament Police separate clashing Brexit protesters outside Parliament Anti-Brexit protester Steve Bray (left) and a pro-Brexit protester argue as they demonstrate outside the Houses of Parliament Getty Images Police separate clashing Brexit protesters outside Parliament A pro-Brexit protester argues Getty Images Police separate clashing Brexit protesters outside Parliament Police surround the pro-Brexit protester after he confronted Steve Bray, a pro-European protester Getty Images Police separate clashing Brexit protesters outside Parliament A leave supporter is spoken to by a police officer as he argues with a remain supporter, Steve Bray, outside Parliament PA Police separate clashing Brexit protesters outside Parliament MPs in Parliament are to vote on Theresa May's Brexit deal next week after her December vote was called off in the face of a major defeat Getty Images Police separate clashing Brexit protesters outside Parliament A leave supporter is spoken to by a police officer PA Police separate clashing Brexit protesters outside Parliament Police look on as anti-Brexit protesters demonstrate outside the Houses of Parliament. Getty Images Police separate clashing Brexit protesters outside Parliament Police hold back a leave supporter PA Police separate clashing Brexit protesters outside Parliament A police officer speaks with anti-Brexit protester Steve Bray Getty Images Police separate clashing Brexit protesters outside Parliament Police surround a pro-Brexit protester after he confronted a pro-European protester Getty Images Police separate clashing Brexit protesters outside Parliament Conservative MP David Davies, wearing a gopro camera, speaks to anti-Brexit protester Steve Bray Getty Images

But Liz Truss, the chief secretary to the Treasury, told ITV's Peston: "I do not support being in a customs union.

"I think it’s hugely problematic and I don’t believe that many of my colleagues in the Conservative party support it."