Opposition MPs will try to change Theresa May’s flagship Brexit legislation to guarantee the UK stays in the single market and the customs union.

An amendment to the EU (Withdrawal) Bill to prevent the Government from using sweeping powers to take Britain out of the EU agreements has been backed by the SNP, the Liberal Democrats, Plaid Cymru and the Green Party.

The move will be likely to expose deep divisions in Labour’s ranks over membership of the single market, days after Jeremy Corbyn came under fire from pro-EU MPs in his own party for taking the option off the table.

Labour MP Wes Streeting, who has been critical of Mr Corbyn’s leadership, used a speech on Saturday to warn that his party’s Brexit policy “stands as the single biggest barrier to the UK’s membership of the single market and customs union”.

It comes after Mr Corbyn was “empty chaired” at a cross-party summit on single-market membership which he refused to attend due to concerns it was “no more than a political gimmick”.

SNP Westminster leader, Ian Blackford, said: “Time is running out to prevent the economic catastrophe of an extreme Tory Brexit.

“We know UK government plans to drag Scotland and the UK out of the single market and customs union would destroy hundreds of thousands of jobs, and cause lasting damage to the incomes, livelihoods and living standards of millions of people across the country.

“With just 10 months to go before a deal is due between the UK and EU, sensible MPs of all parties must now unite to protect our vital place in the single market.”

The bill – which will move EU law onto the statute books after Brexit – returns to the Commons on Tuesday, after passing eight gruelling days of line-by-line scrutiny before Christmas.

It will have its report stage and third reading before moving onto the Lords, where pro-EU peers are expected to make trouble for the Government.

Liberal Democrat leader Sir Vince Cable hailed the amendment as a “significant step in the fight against Brexit”, signalling increased resolve among opposition MPs to join forces against the Government over Brexit.

He said: “Through the four leaders in the House of Commons, we are presenting a united front. We urge the leadership of a fifth opposition party, Labour, to join us so we can change course from the dangerous Brexit being pursued by the Conservatives.”

Plaid Cymru Westminster leader, Liz Saville-Roberts, said: “We remain hopeful that the Labour Party will work with us and take the opportunity to defeat the Tories.”

Green Party co-leader, Caroline Lucas, said: “What happens this year in Parliament will have huge and lasting repercussions for the country – which is why we’re putting party differences aside and working alongside each other.

“We urge the Labour leadership to join us in backing this crucial amendment – and show that they too are willing to put the national interest first.”

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Labour’s official position is that it wants to negotiate a deal with the EU to retain the benefits of the single market, but insists it is not “a membership group” that can be joined after Brexit.

A spokesperson for the Department for Exiting the European Union said: “We respect the four freedoms of the EU and that is why, as we leave the EU, we are leaving the single market and customs union.