Britain's opposition Labour Party says it would back calls for a second referendum on Brexit if Parliament rejects its alternative plan for leaving the European Union.

Key points: Labour MPs won't call for a second vote until Mrs May puts her deal to Parliament

Labour MPs won't call for a second vote until Mrs May puts her deal to Parliament The Opposition's support for a second referendum dulls the threat of a no-deal exit

The Opposition's support for a second referendum dulls the threat of a no-deal exit Britons voted by 52-48 per cent in favour of leaving the EU in 2016

With just over a month until Britain is due to leave the bloc on March 29, Prime Minister Theresa May is seeking changes to her exit deal in order to break an impasse in Parliament.

Labour's decision could damage her hopes of winning support for a revised deal in a vote she has promised by March 12, by attracting those who would have backed her agreement to avoid a no-deal exit but who prefer a second referendum.

Parliament is due to debate and vote on Wednesday on the next steps in Britain's tortuous departure from the EU, and MPs are set to put down proposals, or amendments, which could include demanding the exit deal is put to a public vote.

Britain's Prime Minister Theresa May is approaching her toughest test on Brexit. ( AP: PA )

On Monday (local time) Labour said it would put forward an amendment calling on the Government to adopt its Brexit proposals, which include a permanent customs union with the EU and close alignment with the bloc's single market.

"If Parliament rejects our plan, then Labour will deliver on the promise we made at our annual conference and support a public vote," Labour's Brexit spokesman Keir Starmer said on Twitter.

Parliament is not expected to back Labour's Brexit plan.

Labour said it would support a bid by one of its MPs, Yvette Cooper, to give Parliament the legal power to force Mrs May to delay Brexit by seeking an extension to the Article 50 negotiating period.

"We are committed to also putting forward or supporting an amendment in favour of a public vote to prevent a damaging Tory (Conservative) Brexit being forced on the country," Labour leader Jeremy Corbyn was due to tell a meeting of his MPs on Monday, his office said.

"One way or another, we will do everything in our power to prevent no deal."

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No turning back

That amendment may not come at this week's vote in Parliament however.

A proposal by Labour MPs Peter Kyle and Phil Wilson that Mrs May's deal be put to the public in another referendum will not be put forward for a vote in Parliament until the Prime Minister brings her agreement back for approval.

"There's no turning back for Jeremy now," Mr Kyle said.

Mr Corbyn has been under pressure for some time to support a second referendum. Last week, eight referendum-supporting MPs quit the Labour Party, in part owing to frustration over his failure to back another vote.

A group of Labour MPs quit the Opposition last week over its approach to issues including Brexit and anti-Semitism. ( PA via AP: Stefan Rousseau )

The prospect of holding a second vote poses a dilemma for Mr Corbyn: while many of the party's members and supporters fervently back a so-called People's Vote, others simply want Britain to leave the EU as soon as possible.

Reaction from MPs in the meeting on Monday was split.

It remains unclear whether there is a majority in Parliament in favour of holding another public vote and Labour MP Stephen Kinnock said while he was pleased parliament would get a chance to express its view, he also had concerns.

"I still have deep reservations about the idea of having another referendum. I think it's going to be deeply divisive," he said.

Britons voted by 52-48 per cent in favour of leaving the EU in a referendum in 2016.

The Remain Labour campaign group, which wants to stop Brexit, said the announcement was "a significant step forward".

"A second referendum was only ever possible with the votes of Labour Members of Parliament and we are now on the verge of making this happen," founder Andrew Lewin said in a statement.

"We are not complacent, but we are closer tonight to a People's Vote than we have ever been."

Reuters

