I have done a U-Turn: or, perhaps more accurately, a 360-degree turn. Last Friday, when Sam Gyimah resigned from the government, I said that the chances of another referendum had gone up significantly.

Since then, I have had many more conversations with MPs and I am convinced of two things. The first is that there are, just about, the numbers in the House of Commons to get a second referendum if the Labour party comes out in support of one.

There are at least 16 Labour MPs who would vote against another referendum, and that is a very conservative estimate. (All in all, 25 Labour MPs have rebelled against Jeremy Corbyn to deliver a harder Brexit than the one being offered by the leadership so far, but 16 represents the biggest single rebellion.) That means youd need at least 21 Conservative rebels to overcome the combined might of the Conservative-DUP majority.

Just one Conservative rebellion – the one that passed Dominic Grieves procedural amendment on the meaningful vote – has exceeded the 21-vote mark, with 25 votes. But of those 25 MPs, three are known to be privately opposed while a fourth – Nick Boles – is publicly and vocally opposed. Against that, several Conservative MPs who voted against the Grieve amendment are supportive of the idea of another referendum so we can fairly say that there are, just about, enough Conservative MPs who are open to the idea that it could just pass.

Equally important to the shifting arithmetic is retirement. Several Labour MPs who are in heavily pro-Leave seats have said to me that they are now more open to voting to re-open the question as they dont expect their parliamentary careers to continue after the next election in any case, when even a few weeks ago they were saying they would, in the event that the Labour party were to support another referendum, vote against re-running the referendum.

So there is a small but significant shift in parliament which means that another vote might be able to command the support of a majority of MPs. But thats not the only barrier to another vote.

To get another referendum you dont only need to be able to cobble together a majority of MPs in Parliament: you need to pass a referendum act through the Houses of Parliament. But the legislative timetable is controlled by the executive, not by the legislature itself.

So you need not just a majority in Parliament for another referendum, but a majority within the ruling party to permit that referendum to take place without seeking to remove that leader. And its clear that, among committed pro-Brexit MPs who have not yet tried to remove Theresa May, re-opening the referendum question is, for the moment, not something they are willing to stomach.

It comes back to the big problem of negotiating the United Kingdoms exit from the European Union in this parliament. It has to be acceptable to two majorities, a majority of the Conservative Party and a majority in the House, as well as to the 27 nations of the European Union. And it is not clear that such a Brexit exists.

Stephen Bush is special correspondent at the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to domestic and global politics.

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