The prime minister's precarious position as Brexit negotiations reach a critical juncture

So here is some logical deduction on Tuesday's Brexit events. Please feel free to tell me where I am getting it wrong.

1) If the leaks of the draft agreement on the EU divorce/transition deal are right, there is no way the UK government can accept a legally binding pledge to put a border in the middle of the Irish sea, rather than in the middle of the island of Ireland, in any circumstances. Apart from anything else, the DUP won't let them.

2) The government needs a transition deal, otherwise business leaders are really going to start to worry.

3) The Labour Party's conversion to a Customs Union means there will almost certainly be a vote on the matter in the House of Commons at some stage in the next three or four months (possibly on the EU Withdrawal Bill, which could be amended in the Lords). It seems more than possible the government will lose this.

Hard Brexiteers like Boris Johnson will react furiously if the UK signs up to the customs union. Credit: PA

4) There is thus a powerful logic for the Prime Minister to accept we will remain a member of the Customs Union relatively soon. This doesn't entirely solve the Irish border question, but it would take the heat out of it and get us through to a transition deal. And she could still claim we were controlling immigration and recovering some sovereignty.

5) Tory Brexiteers would absolutely hate this. For many, the ability to do trade deals is half the reason for leaving. It could well precipitate a leadership challenge.

6) But even if an out and out Brexiteer won the ensuing contest, he or she would face the same parliamentary arithmetic.

A firm decision could spark a leadership contest - or another referendum. Credit: PA

7) So far, the Prime Minister has kept going by fudging almost every key issue in relation to Brexit, but it feels like we are now at the point where the maths in the House of Commons becomes critical. And it is just hard to see how she has the numbers for the Brexit she wants. Thus, something must give.

8) If she ends up having to accept we remain part of the Customs Union, she will be well on the way to a deal that almost no one favours - not Remainers clearly, but not all that many Leavers either. This seems to make a further referendum more likely.