Brexit: EU's Guy Verhofstadt welcomes Jeremy Corbyn's offer to Theresa May

Jeremy Corbyn's letter setting out his party's demands for supporting a Brexit deal has been welcomed by the European Parliament's Brexit co-ordinator.

Guy Verhofstadt said "the broadest possible majority" was needed for a Brexit deal in the UK.

An EU source said European Council President Donald Tusk said the letter was a "promising way" out of the impasse, in talks with the PM.

But Mr Corbyn's stance has upset Labour supporters of another referendum.

MP Owen Smith has said he and "lots of other people" were considering their future in the party as a result.

The UK is due to leave the EU on 29 March when the two-year limit on withdrawal negotiations under the Article 50 process expires.

But Prime Minister Theresa May is struggling to get the withdrawal deal she has negotiated with the EU through Parliament - MPs rejected it by a historic margin last month.

Mr Corbyn wrote to her on Wednesday spelling out his party's five demands for supporting a deal. These included a "permanent and comprehensive UK-wide customs union" aligned with the EU's customs rules, but with an agreement "that includes a UK say on future EU trade deals".

The letter does not mention previous demands that any deal must deliver the "exact same benefits" that membership of the single market and customs union currently does - effectively scrapping the party's "six tests" that had been its Brexit policy.

Mrs May has been in Brussels holding talks with Mr Tusk, Mr Verhofstadt, European Parliament President Antonio Tajani and European Commission President Jean-Claude Juncker.

Mr Verhofstadt told a press conference: "We can't have an agreement with uncertainty in the UK based on majorities of six, seven, eight or nine votes in the House of Commons.

"A cross-party co-operation is the way forward and I think I can say that we welcome also the letter that Jeremy Corbyn has written today to Mrs May to offer such a cross-party exit.

"It's important now that this leads to a position in the UK that has the broadest possible majority, so that we can conclude these negotiations."

However, it was criticised by Labour members of the People's Vote campaign for another EU referendum, who said Mr Corbyn had gone back on a commitment to back a public vote, if he cannot force a general election.

Mr Smith, who challenged Mr Corbyn for the Labour leadership in 2016, 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."

Another pro-EU Labour MP, Chuka Umunna, said: "This is not opposition, it is the facilitation of a deal which will make this country poorer."

But Labour's Stephen Kinnock, who backs the "Norway Plus" model of a close economic partnership with the EU, welcomed Mr Corbyn's letter, tweeting: "This can break the deadlock."

And the Conservative former cabinet minister Sir Oliver Letwin, who also favours a Norway-style agreement, said it could be the basis of a cross-party deal.

Labour shadow Brexit secretary Sir Keir Starmer told the BBC: "What this letter does is to set out in clear terms that the prime minister needs to abandon her Brexit red lines.

"It does not rule out the option of a second referendum - a public vote - and Jeremy Corbyn will be writing to members today to remind them about that."

A senior No 10 source said the government was "looking at those proposals but there are obviously very considerable points of difference that exist between us.

"The PM continues to believe an independent trade policy is one of the key advantages of Brexit."