Theresa May faces a major headache when the House of Lords attempts to engineer a ‘soft Brexit’ by keeping the UK in the single market.

The unelected upper chamber has already inflicted a series of embarrassing defeats on the government as it tries to pass the EU Withdrawal Bill – the piece of legislation that will make Brexit happen.

But the latest stand-off on Tuesday could be the most humiliating yet, and raise serious questions over May’s premiership if she fails to reverse the Lords amendment by losing a vote in the House of Commons.

Jeremy Corbyn is facing his own rebellion, with Labour peers threatening to defy party orders to abstain from the crunch vote.

What’s happening?

On Tuesday, the House of Lords votes on a series of amendments to the government’s Brexit bill.

Peers have already voted for the UK to remain part of a European customs union, meaning no customs checks and EU citizens’ rights to be protected after the UK quits.

But now they want to go further by pushing for an even softer Brexit by keeping the UK in the single market – the very opposite of what May has repeatedly promised to do.

Their amendments, if successful, would instruct the government to begin negotiating future UK membership of the European Economic Area (EEA).

This arrangement has been described as the “Norway option” – full access to the EU’s internal trading market, but outside the union itself.

Brexiteers won’t like it

May herself has complained that the Lords has “thwarted” the will of the people in the referendum by orchestrating defeats to the Bill that now run into double figures.

But EEA membership would pose an even bigger problem, undermining a key tenet of her Brexit policy. The arrangement is seen as the worst of all worlds by leading Brexiteers such as Jacob Rees-Mogg. 

While proponents argue the UK would be able to strike its own deal on freedom of movement, and still be inside the EU’s internal market, critics say an EEA affiliation would mirror EU regulations and European Court of Justice rulings, but without any say in decision making.

Rees-Mogg and other Eurosceptics argue that it would leave the UK as “a vassal state” – which is a Shakespearean way of saying the country would be in a subordinate position to Brussels, which isn’t really Brexit at all.

Trouble for the Labour Party

Labour has also managed to get itself in tangle ahead of the vote.

The party’s policy, as Jeremy Corbyn has laid out, is to support the UK being in a customs union with the EU, but not in the single market or have EEA membership.

In line with that stance, the party’s group in the House of Lords has been ordered to fall into line – whipped to abstain when it comes to the vote on Tuesday.

But reports at the weekend suggested more than 40 Labour peers are ready to back the cross-party EEA amendment.

Businessman and Labour peer Lord Waheed Alli, who has put his name to the amendment, said: “This is complete cowardice. There is no point in being in politics to abstain.

“If you stand in the middle of the road someone is going to knock you over.”

Former shadow cabinet minister and Labour MP Chuka Umunna said it would “go against Labour’s progressive values” not to back the move.

But Corbyn’s allies have signalled peers are expected to tow the line. Shadow international trade secretary Barry Gardiner said such an arrangement would reduce the UK to being a “rule taker” without a seat at the table when decisions on regulations are made.

Next stop: the House of Commons

A government with a healthy majority and loyal backbenchers could be expected to overturn a Lords amendment when it ping-pongs back to the House of Commons. But May has neither.

Around 10 pro-European Tory MPs having spoken supportively in the past about EEA membership, enough to pass to keep the amendment in the Bill. The Prime Minister could then be relying on support from Labour MPs to stamp out the ‘Norway model’.

The ball would then be back in Jeremy Corbyn’s court. His top team have been accused of “constructive ambiguity” on Brexit, a flexible and sometimes confusing position that has allowed the party to both appeal to their pro-Brexit heartlands while showing enough leg to the largely europhile younger generation that has flocked to the Labour leader. But it would not be able to fudge for much longer.

The party would face a tricky decision: continue to oppose EEA and ease the pressure on May, or back the Lords and deliver a potentially fatal blow to the PM. In either scenario it faces a backlash.

The end for Theresa May?

The Lords vote is just one of a series of Brexit-related pressures being piled on the PM, including splits within the Cabinet over a preferred option of a customs relationship with Europe and concerns over the Irish border. But defeat in the Commons would be a hammerblow to her authority.

In the background always lurks the powerful European Research Group, a cabal of more than 60 backbench Tory MPs, led by Rees-Mogg, who could force a leadership contest if they are unhappy with the government’s progress on Brexit.