Jeremy Corbyn is facing claims that Labour MPs and members could quit the party over his stance on Brexit.

The Labour leader has written to the Prime Minister setting out five demands that need to be met to get his party’s support for a Brexit deal.

But Owen Smith, his former leadership rival, said he was considering his position in the party and hit out at the prospect of Labour MPs being asked to back a deal which he said would damage livelihoods.

Other pro-EU MPs also criticised Mr Corbyn’s plan, claiming it was a change to the party’s policy of keeping open the prospect of a second referendum if Labour couldn’t force a general election.

Shadow Brexit secretary Sir Keir Starmer insisted the move by Mr Corbyn did not take the option of a so-called People’s Vote off the table.

Downing Street, however, said ministers were looking at the proposals “with interest” – although there were still “very considerable points of difference” between them.

In his letter to Mrs May, the Labour leader set out five demands:

–  A permanent customs union to deliver frictionless trade and help avoid a hard border on the island of Ireland

– Close alignment with the single market, including shared institutions and obligations

– Alignment on rights and protections so that UK standards keep pace with those across Europe as a minimum

– Participation in EU agencies and funding programmes,

–  Unambiguous agreements on the detail of future security arrangements, including access to the European Arrest Warrant and vital shared databases.

On a visit to Worcester, Mr Corbyn told reporters: “Half of our trade is with Europe. A lot of our manufacturing industries are very frightened, very worried at the moment that on March 29 there’ll be a cliff edge.

“There cannot be a cliff edge. We will do everything we can in Parliament to prevent this cliff edge exit.”

But Mr Smith, who stood against Mr Corbyn in 2016, said he was considering his future in the party.

“I think it’s something that I and lots of other people are considering right now,” he told BBC Radio 5 Live.

“At the moment I may be asked by the Labour Party to row in behind a policy decision that they know, and the Government knows, is going to make the people I represent poorer and – more fundamentally actually – is at odds with the internationalist, social democratic values I believe in.”

Prominent pro-EU MP Chuka Umunna said the position was “totally demoralising”.

He said: “This is not Opposition, it is the facilitation of a deal which will make this country poorer.”

He added: “I hate to think what all those young voters who flocked to the party for the first time in 2017 will make of this.

“Vote Labour, get a Tory Brexit. They will feel they have been sold down the river.”

Shadow international trade secretary Barry Gardiner defended the shift in policy away from the six tests Labour originally set for a Brexit deal, saying the offer was made “in a spirit of co-operation and compromise”.

“It’s not about tests now,” he told BBC Radio 4’s Today programme. “What we are doing is saying we believe that these are the options that are available that would actually secure a majority in the House of Commons.”

Sir Keir said the letter “sets out in robust terms that the Prime Minister must abandon her Brexit red lines”.

“It does not take the option of a public vote off the table.”

Matthew Pennycook, a member of Sir Keir’s frontbench shadow Brexit team, said if Mrs May did not accept Labour’s terms “we must move to support a public vote”.

There were “no other credible options left” to prevent a no-deal Brexit.

A senior No 10 source said it was “welcome” that Mr Corbyn was prepared to engage on the issue.

“We are looking at those proposals with interest but there are obviously very considerable points of difference that exit between us,” the source said.

“The PM continues to believe that an independent trade policy is one of the key advantages of Brexit. Her position on the customs union hasn’t changed.”

Mrs May’s effective deputy prime minister, David Lidington, said the Labour plan for a customs union with a say in EU trade deals was “wishful thinking”.

In Brussels, a European Commission spokesman declined to discuss Mr Corbyn’s proposals, saying only: “Our interlocutor is Her Majesty’s Government and the Prime Minister.”

On Wednesday European Commission president Donald Tusk highlighted Mr Corbyn’s “pro-Brexit stance” and said “there is no political force and no effective leadership for Remain”.