Jeremy Corbyn and Theresa May had to face up to an inconvenient truth last week: they both basically agree about Brexit. Not just on the need for the UK to honour the referendum and leave the European Union, but also about remaining in a customs union.

Corbyn calls it a “permanent customs union” while the Prime Minister calls it a “common customs territory” as part of the Irish backstop. Both mean essentially the same thing: that Britain would remain in a customs union with the EU unless and until a better option comes along.

The Labour leader’s “six tests”, of which the crucial one was that any deal had to have “exactly the same benefits” as full membership of the single market, have been dropped.

He talks now of “dynamic alignment” with the rules of the single market. But May also envisaged a “common rule book” in her Chequers plan, which comes to much the same thing.

Both are committed to ending free movement. Most importantly, Corbyn now accepts May’s Withdrawal Agreement, provided there is this bespoke customs union.

A visitor from another planet – or from Brussels which comes to much the same thing – would be astonished that the two of them have failed to come up with a common negotiating position.

However, the political reality is that it would be suicide for May and Corbyn to recognise that they are essentially talking the same language, which is why immense efforts were being made last week to make them sound as if they are worlds apart.

The Conservative Party has long suspected that the Withdrawal Agreement basically commits the UK to remain in the EU Customs Union indefinitely, and this is almost certainly the case.

So long as the UK agrees to avoid a hard border in Northern Ireland, and observe the spirit of the Good Friday Agreement, then it has to accept a common customs arrangement and alignment with the rules of the single market. That is all spelled out clearly in the Withdrawal Agreement.

Some magic formula might arise in future to allow a friction-free border in Ireland, but no-one has managed to come up with one so far. But for Theresa May to formally agree a customs union would destroy the Tory party and lead to mass Cabinet resignations.

And curiously, if Jeremy Corbyn were to strike a deal with the PM along the lines of Labour’s own policy, it would also split his party apart.

It is already deeply fractured over the question of a referendum. We are in a land of broken mirrors.

A People’s Vote was never part of Labour’s original Brexit demands but for many, like the shadow foreign secretary Emily Thornberry, it has now assumed make-or-break significance.

The Labour membership, led by the now rehabilitated ultra-Blairite, Alastair Campbell, demands it, even though it is not entirely clear that a repeat referendum would deliver a different result to 2016.

Of course, it is now generally referred to as a “confirmatory referendum” on whatever deal Corbyn and May might come up with.

The proposal from Labour is that the referendum would only offer one alternative: Remain. This is almost certainly for the birds, because Brexiteers would surely take to the streets if a repeat referendum were to be staged without the option of voting for No Deal, which for many of them is what Brexit means.

Fortunately for him, Corbyn is so vague and indecisive, that he will probably be spared the indignity of having to agree with Theresa May. This is one moment when the Labour leader’s incoherence and lack of leadership ability comes to the aid of the party by leaving everyone totally confused.

But again, looked at from Brussels, it seems blindingly obvious that May and Corbyn should listen to the Chancellor, Philip Hammond, and put a repeat referendum motion to Parliament under both their signatures.

This would probably mean it gets passed. In last week’s indicative votes, the confirmatory ballot motion registered the largest number of supporters. Mind you, Parliament is so febrile, nothing is certain.

The House of Commons seems determined to reject every proposal put before it.

Parliament has become so dysfunctional, with naked bottoms, the Speaker’s diction and the liquid inundations, that expectations of this house of comedy are dismally low.

If Corbyn agreed a referendum, around 25 pro-Brexit Labour MPs, and key figures like the party chairman Ian Lavery, would certainly rebel, and probably more.

There are more pro-Brexit MPs on the opposition benches than Labour has recognised.

The one thing Parliament has agreed – by one vote – is that there should be an extension to A50.

This, of course, is a statement of the bleedin’ obvious, since leaving on Friday would be almost criminally insane.

Even No Dealers realise a delay is necessary, and Brussels certainly does. May has again proposed a delay until June 20, which she knows will be rejected by Brussels.

It will have to be a year-long “flextension” or No Deal.

So, this week will be all about how long Brussels decides Britain should remain in the UK.

That it has come to this is a perfect illustration of the madness of the Brexit process.

There has been talk of the EU saying: enough is enough – it’s time to end the madness and get the UK out. It doesn’t want a lot of rowdy Brexit MEPs to be elected to the European Parliament next month, and is afraid of the Brexit contagion spreading.

However, it’s most unlikely that the EU will emulate the climate protesters and give the UK the bum’s rush.

It is always said that Brussels will never force a member to leave if it can possibly avoid it.

There is every chance that a long extension will lead to an election and/or a referendum.

And there is another intriguing possibility: that the European elections could turn into a de facto referendum on remaining in the UK. In fact, there might even be a case for the Government to hold a “special measures” referendum on the same day.

For the truth is that the customs union is an unsatisfactory compromise.

It is confined to trade in physical goods, and 80% of the UK economy is services. Britain would be a rule taker without any say in trade policy and would not be able – as is the case with Norway – to conduct its own trade deals. Britain would have to observe most of the single market rules anyway, so why not have the benefits of membership?

Indeed, the more you look at the way the debate has moved, the more obvious the solution to Britain’s problems becomes remaining in the European Union under our current highly advantageous terms.

Britain has a very good deal already, with opt-outs from things like the single currency and a veto in the council.

If that case were put convincingly in a referendum, we might end up with an exhausted nation deciding on the most obvious course: to revoke Article 50 and go back to some kind of normality.

If not, it looks like a Hotel California Brexit: you can check out but you can never leave.