Now that Michel Barnier has rejected Theresa May’s proposed customs arrangement with the EU, her Chequers blueprint looks dead.

Indeed, the minds of Conservative ministers and MPs are turning to another possible escape route from the Brexit maze: the UK staying in the single market by remaining in the European Economic Area (EEA) along with Norway, Iceland and Liechtenstein.

Significantly, this option is not just being discussed by the band of 20 pro-European Tory MPs led by Dominic Grieve. It is also attracting the attention of pragmatic Brexiteers, whose unofficial leader is Michael Gove.

While he is staying loyal to May and her Chequers plan for now, some allies can envisage Gove backing EEA membership in the autumn if, as looks increasingly likely, May cannot seal a deal with the EU or win parliament’s backing for one.

Pro-EU Tories would stay in the single market permanently. (So would I; it undoubtedly brings economic benefits.) But pragmatic Brexiteers would probably insist the move was temporary – and limited to four or five years – in order to win over as many Tory MPs as possible.

Unlike the options currently on the table, the EEA plan would stand a good chance of getting through parliament. Labour wants “full access” to the single market, but would have a dilemma. While Jeremy Corbyn might urge his MPs not to rescue the Tories from their own Brexit mess and to hold out for a general election, many Labour MPs, trade unions and party members might be tempted to take the EEA route. So would the SNP and Liberal Democrats.

The proposal would provide some much-needed stability for business, as it would cover services (which account for 80 per cent of the economy) as well as goods, and so would cushion Brexit’s impact. Crucially, as an “off the shelf” solution, it would be acceptable to the EU. It would prevent the UK crashing out next March without a deal, and give the UK time to prepare for its long-term destination.

An attraction for Brexiteers is that the UK would be outside the EU's remit on agriculture, fisheries, home and foreign affairs. The move would help solve the Irish border problem, although there would still need to be agreement on customs – probably a compromise that the EU would call a customs union while the government would not.

The downside is that the UK would seek some flexibility over EEA rules on free movement (though some restrictions are already allowed). The UK might win more favourable terms than Norway because of its economic clout. If that didn’t happen, the government could apply an emergency brake to EU migration.

While the EEA path might steer the UK away from a disastrous cliff-edge exit, it would almost certainly not be good news for May. In the chatter among Tories, there is a recognition it would be a U-turn too far for her, and that she would have to go.

On becoming prime minister two years ago, she prematurely ruled out single market membership in an attempt to reassure Leavers she was no longer a Remainer, and appeal to Labour’s working class vote on immigration. We could have had a much better debate on Brexit if she had not done so, but never mind.

If a majority of Tory MPs coalesce around the EEA option, they would then have the numbers to defeat her in a vote of confidence as party leader.

Brexit threatens life on the Irish border: in pictures Show all 15 1 /15 Brexit threatens life on the Irish border: in pictures Brexit threatens life on the Irish border: in pictures An abandoned shop is seen in Mullan, Co Monaghan. The building was home to four families who left during the Troubles. The town was largely abandoned after the hard border was put in place during the conflict. Mullan has seen some regeneration in recent years, but faces an uncertain future with Brexit on the horizon Reuters Brexit threatens life on the Irish border: in pictures A defaced ‘Welcome to Northern Ireland’ sign stands on the border in Middletown, Co Armagh Reuters Brexit threatens life on the Irish border: in pictures Mervyn Johnson owns a garage in the border town of Pettigo, which straddles the counties of Donegal and Fermanagh. ‘I’ve been here since 1956, it was a bit of a problem for a few years. My premises has been blown up about six or seven times, we just kept building and starting again,’ Johnson said laughing. ‘We just got used to it [the hard border] really but now that it’s gone, we wouldn't like it back again’ Reuters Brexit threatens life on the Irish border: in pictures Farmer Gordon Crockett’s Coshquin farm straddles both Derry/Londonderry in the North and Donegal in the Republic. ‘At the minute there is no real problem, you can cross the border as free as you want. We could cross it six or eight times a day,’ said Crockett. ‘If there was any sort of obstruction it would slow down our work every day’ Reuters Brexit threatens life on the Irish border: in pictures John Murphy flies the European flag outside his home near the border village of Forkhill, Co Armagh Reuters Brexit threatens life on the Irish border: in pictures Potter Brenda McGinn stands outside her Mullan, Co Monaghan, studio – the former Jas Boylan shoe factory which was the main employer in the area until it shut down due to the Troubles. ‘When I came back, this would have been somewhere you would have driven through and have been quite sad. It was a decrepit looking village,’ said McGinn, whose Busy Bee Ceramics is one of a handful of enterprises restoring life to the community. ‘Now this is a revitalised, old hidden village’ Reuters Brexit threatens life on the Irish border: in pictures Union Flag colours painted on kerbstones and bus-stops along the border village of Newbuildings, Co Derry/Londonderry Reuters Brexit threatens life on the Irish border: in pictures Grass reflected in Lattone Lough, which is split by the border between Cavan and Fermanagh, seen from near Ballinacor, Northern Ireland Reuters Brexit threatens life on the Irish border: in pictures Donegalman David McClintock sits in the Border Cafe in the village of Muff, which straddles Donegal and Derry/Londonderry Reuters Brexit threatens life on the Irish border: in pictures An old Irish phone box stands alongside a bus stop in the border town of Glaslough, Co Monaghan Reuters Brexit threatens life on the Irish border: in pictures Billboards are viewed from inside a disused customs hut in Carrickcarnon, Co Down, on the border with Co Louth in the Republic Reuters Brexit threatens life on the Irish border: in pictures Seamus McQuaid takes packages that locals on the Irish side of the border have delivered to his business, McQuaid Auto-Parts, to save money on postal fees, near the Co Fermanagh village of Newtownbutler. ‘I live in the south but the business is in the North,’ said McQaid. "I wholesale into the Republic of Ireland so if there’s duty, I’ll have to set up a company 200 yards up the road to sell to my customers. I’ll have to bring the same product in through Dublin instead of Belfast’ Reuters Brexit threatens life on the Irish border: in pictures A disused Great Northern Railway line and station that was for customs and excise on the border town of Glenfarne, Co Leitrim Reuters Brexit threatens life on the Irish border: in pictures Alice Mullen, from Monaghan in the Republic of Ireland, does her shopping at a former customs post on the border in Middletown, Co Armagh. ‘I’d be very worried if it was a hard border, I remember when people were divided. I would be very afraid of the threat to the peace process, it was a dreadful time to live through. Even to go to mass on a Sunday, you’d have to go through checkpoints. It is terribly stressful,’ said Mullen. ‘All those barricades and boundaries were pulled down. I see it as a huge big exercise of trust and I do believe everyone breathed a sigh of relief’ Reuters Brexit threatens life on the Irish border: in pictures A bus stop and red post box stand in the border town of Jonesborough, Co Armagh Reuters

Eurosceptics have not always been hostile to the single market. Archives from 1988 released this week remind us of Margaret Thatcher’s “deep enthusiasm” for it.

Boris Johnson said in 2013 when he was London mayor: “I’d vote to stay in the single market. I’m in favour of the single market. I want us to be able to trade freely with our European friends and partners.” Daniel Hannan, the Tory MEP and one of Brexit’s architects, believes an EEA-type deal would reflect the close result in the 2016 referendum, and be much better than a customs union because the UK could run an independent trade policy.

However, not all Brexiteers would support EEA membership. Even if Gove promised it would be temporary, hardliners would fear it would become permanent. Their figurehead would almost certainly be Boris.

He did not attack May head-on in his Commons resignation statement; for all his grumbling about her Chequers plan, he has not produced an alternative. Allies say he will do this over the summer, and be ready with one for the Tory conference at the end of September. It will likely be a free trade deal similar to the “Canada plus plus plus” version favoured by David Davis.

In the absence of a withdrawal agreement, or if parliament rejected both a May deal and no-deal exit, the Gove and Boris camps might agree to pull the plug on May. She might even jump before she was pushed. That would raise the intriguing prospect of another twist in the Gove-Boris drama: a Tory leadership election between them, to decide whether the government opts for EEA membership or a Canada-EU style deal.