For months, everyone and their mother has been calling Brexit “Groundhog Day”. However, what they forget is that, in the eponymous film, the day does actually come to an end – when Bill Murray ends up in bed with Andie MacDowell. It’s looking as if Brexit Day might end up in a similarly way: with Jeremy Corbyn in bed with Theresa May. Politically, I hasten to add, since that is a disturbing image for a Sunday morning.

Last week, Corbyn made a remarkable overture to the Prime Minister. He effectively dropped his opposition to her Withdrawal Agreement, which Labour had repeatedly condemned as the “worst of all worlds”. The Labour leader’s letter still calls for a customs union, regulatory alignment on trade and guarantees on workers' rights and security cooperation. But, crucially, Labour is no longer holding to the “six tests”, and insisting a Brexit deal should deliver “exactly the same benefits” as being in the single market.

Labour has even dropped its opposition to the Irish backstop, which Mr Corbyn condemned, as recently as December, for leaving Britain “in an indefinite halfway house with no say on its future”. The explanatory note that Labour circulated after the leader’s letter to May is quite clear. “Any withdrawal agreement," it says, “will need to include a backstop." Labour is also hinting at further compromises in “negotiations”.

Hitherto, Labour’s policy has been to make demands May could never accept; now they are trying to make her an offer she can’t refuse.

So at last, after months of there being nothing much new to say about Brexit, suddenly we have what looks like a breakthrough, a historic compromise. Of course, you can’t overestimate the ability of political leaders to look a gift horse in the mouth. Theresa May may be so wedded to being a “bloody difficult woman” (as she describes herself) that she may find a way to avoid accepting Labour’s free hooved mammal. But the deal is there to be made.

Senior Tories like Sir Oliver Letwin have welcomed the Labour offer, seeing it as a step towards a Norway-style agreement, even though it isn’t. Labour’s plan is much closer to Turkey, which is also in a customs union and accepts regulatory alignment. Brussels likes Corbyn's proposals too, as a way out of hard Brexit “hell”.

I've argued that the logic of Labour’s position was always to back something resembling Theresa May’s deal with the EU. It corresponds to Labour’s manifesto commitments to leaving the EU, including the single market, and ending free movement while seeking frictionless trade. Mrs May has always supported regulatory alignment, since the “common rule book” in her Chequers plan. And the backstop, remember, involves the UK remaining in the customs union until there is a future comprehensive trade deal.

In what could almost have been a coordinated intervention last week, Mrs May restated in Dublin her determination to prevent a hard border in Ireland. This put the wind up the DUP, since they fear that the border might now move to the Irish Sea.

It didn’t appeal to the hardline Brexiteers in her own party either, who are adamant that no deal is better than her bad deal. They thought it had been killed off by last month’s record-breaking Commons defeat – but it may now live again with Labour’s backing.

They can’t admit it, of course, but May and Corbyn are now speaking broadly the same language. The customs union, regulatory alignment, rights and protections etc are all matters to do with the future trade relationship with the EU, not the Withdrawal Agreement. It covers only money, citizenship and the Good Friday Agreement.

The trading relationship can only be negotiated after Brexit. It is to be hammered out within the up to four years of the transition period, during which the UK remains in the single market and the customs union.

Only if there is no agreement does the backstop comes into play, and that really just extends the transition period indefinitely. May has said she will get assurances that the backstop will be time-limited, but she can’t get that from the European Union. If it was limited, it would no longer be a backstop.

What hard Brexiteers really fear is that the transition period might lead to a soft Brexit, not a clean break – and they are right. What we know is that MPs will block any no-deal Brexit. Hardliners face a choice of May/Corbyn or no Brexit at all.

To secure a Commons majority without them, Mrs May could promise legislation to keep Britain in regulatory alignment with the customs union until a new trade deal is finalised – one which delivers the same benefits. This is anyway implicit in her promises to keep trade “frictionless”. Indeed, remaining in a customs union is the only way of achieving this. Up to now, she hasn’t been able to say this openly for fear of a rebellion by her hardline backbenchers, led by Jacob Rees-Mogg. They want a managed no-deal now, or in four years, under the so-called “Malthouse Plan”.

But if she has an ounce of political sense, May will now face them down and pivot to Labour’s softish Brexit. Labour’s demand that she put the customs union in primary legislation can be finessed, because the trade negotiations can’t happen until after Brexit. She doesn’t even need to ensure that Labour votes with her. Labour could abstain in the meaningful vote and achieve essentially the same result. The DUP would accept the customs union as a guarantee against a backstop or an east/west hard border.

Jeremy Corbyn could explain Labour’s abstention, which will be attacked by Vote Leave MPs and Guardian leader writers, by saying, as his spokespeople did last week: that the top priority “for the nation” is to avoid a no-deal. Corbynite commentators can be relied upon to condemn any Labour MPs who continue to vote against May’s deal as traitors. Unreconstructed Blairites, voting with the hated Moggists to force a no-deal disaster.

Corbyn’s letter made no reference to a People's Vote. Remainers in the Labour Party realise where all this is heading, which is why a number, like former shadow cabinet figures like Owen Smith, and Clive Lewis, have threatened to leave the party. That could become part of the script.

Corbyn has used the Brexit issue to smoke out Blairite Remainers like Chuka Umunna, and the Jewish MP, Luciana Berger, in order to portray them as disloyal splitters.

Of course, ordinary members of the Labour Party will be mightily confused. Many of them still think Labour is committed to a referendum. It still could come to that, of course, if May doesn’t seize this opportunity.

I still harbour vague hopes that A50 could be revoked, but I’m afraid that pro-Europeans are on the wrong side of history right now. The country is destined to leave the EU, because let’s face it, Labour under Jeremy Corbyn is and has always been a pro-Brexit party.

And after Brexit Day? Well, get ready for Groundhog Day 2 as negotiations over the future EU trade deal begin all over again.