1 April 2019 was the last time MPs voted on a referendum. The idea of a ‘confirmatory vote’ failed by a majority of twelve during the indicative votes process: 280 MPs voted for Peter Kyle’s proposal to marry May’s deal with a public vote; 292 voted against; and a further 66 MPs – including all members of the cabinet, under instruction to do so – abstained.

It is fair to say half a year is a long time in Brexit politics. Since then, Labour Party policy has changed to backing a referendum under all circumstances.

Conservative Party policy has moved from backing May’s deal, to Johnson’s proposals, and could soon evolve into a more explicit no deal position.

The Liberal Democrat parliamentary party has nearly doubled in size while shifting its stance to a revoke position, and 7% of MPs who were Conservative MPs in April are now independent MPs.

As a result, the arithmetic may well have shifted in favour of the ‘confirmatory referendum’ idea since April. But exactly what are the numerical and practical hurdles, and are they still too high?

Unless the Tory Party splits again, the numbers are difficult to envisage

Advocates of a referendum might start by fishing in that pool of 66 MPs who abstained on a referendum in April. However, 11 of this group are in Johnson’s cabinet. Another three who aren’t – Penny Mordaunt, Liam Fox and Chris Grayling – supported Brexit.

So that leaves 52 MPs, and it therefore would require a pretty high success rate of 77% to get an extra 40 MPs to now support a public vote.

The first place to start would be those newly-independent 22 Tory MPs – the 21 who lost the whip, and Amber Rudd who did so voluntarily. These MPs are firmly against no deal and, now they are without a party, clearly with an incentive to avoid an election any time soon. However, 9 of these MPs already voted for a referendum in April, while 3 – Nicholas Soames, Richard Benyon and Rory Stewart – voted against the idea.

They could, however, have luck among the remaining 10: Amber Rudd and David Gauke are the latest MPs to suggest they could (reluctantly) support a referendum, along with Oliver Letwin and Ken Clarke.

Then, it’s worth looking at an underappreciated grouping. The SNP – renowned for their unity and discipline in the House of Commons – split on a referendum in April, with four of their MPs abstaining.

This could have been for a couple of reasons: a preference for revoking Article 50, or a feeling that Brexit makes independence more likely. However, it is likely that these MPs are persuadable.

The next step would be to look at the 16 Labour MPs who abstained on a referendum in April. Two of these MPs (along with two who voted for a referendum) are among the 19 who sent a letter to Michel Barnier urging talks to continue.

But many (though not all) of these MPs – including, for example, shadow cabinet members like Jon Trickett – are now on board with a referendum, particularly set against the binary choice of no deal.

However, once you get past these figures to around 25 MPs, advocates of a referendum then get stuck. A majority for a referendum would require a significant chunk of Conservative MPs who are still in the party to either rebel or abstain (and presumably, as a consequence, join their ex-colleagues outside the party).

There are 15 Conservative MPs who previously abstained on a before, only three of whom did so because they were bound by collective cabinet responsibility to abstain. A further 16 voted against a referendum, but also in favour of a customs union.

Many of these names probably overlap with the One Nation group who are now pushing back against the prospect of no deal being in the Conservative manifesto. The sequencing of a referendum before an election is a difficult sell to these MPs.

The clear sense is that they are instead gambling on the Conservative electoral position again expressing a preference for a deal – a manifesto that, if published, would mean those advocating a referendum prior to a general election would already have lost.

1 April referendum abstainers that would need to switch to a pro-referendum position

How could a vote on a referendum come about?

There are two immediate options open to MPs: amending the upcoming Queen’s Speech to include a vote that would indicate Parliamentary support for a referendum, or creating time through the now-ubiquitous Standing Order 24 – which allows backbenchers to take control of the Commons timetable – or amending upcoming ‘Business of the House’ motions, for referendum legislation to be passed

The first option would echo a similar amendment that John Bercow allowed – against a precedent that set the maximum number of Queen’s Speech amendments at two – in favour of a referendum in 2013. However, this would only indicate Parliamentary support for a referendum in the abstract as part of the governing programme, and creates no legal obligation on the government to introduce legislation for one.

An alternative would be to take control of the order paper either before or after the European Council: the government will need to introduce a business motion for the House of Commons to sit on Saturday 19 October, and MPs could amend it to ensure it is a day when MPs control the timetable.

This would make the key pinch-point earlier than Saturday next week: if the numbers existed to take control of the order paper for that purpose (big if), they would then in theory be there for subsequent legislation rushed through the House of Commons.

However, this is not nailed on: for example, in April, the opposition and Conservative rebels won and lost separate Business of the House Motions on the same day. With numbers for a referendum tight (if they exist at all) a couple of MPs getting cold feet could prove decisive.

If a referendum vote passed, what would need to happen next?

Advocates of a referendum, for example Tony Blair, have made it clear they think a referendum is possible without a change in government.

As UCL’s Constitution Unit set out, some of the practical aspects of a referendum – the referendum question, the franchise, any amendments to the regulatory framework, conduct rules for the poll and the date on which the referendum will be held – would need to be dealt with through primary legislation, or short-circuited through repealing the legislation that governs referendums.

A referendum would require spending public money to make it happen: unless standing order 50(1) is removed or is reinterpreted by John Bercow, this requires a government minister to introduce a money resolution after any bill passed second reading.

As a result, it will be difficult (though not impossible) for referendum advocates to cut out the difficult decisions facing opposition MPs about removing the government. A further chunk of MPs against no deal in the Conservative Party would probably have to face a referendum they do not want, as well as the prospect of walking through exit door of the Conservative Party. While advocates may say it remains the best way out, it certainly isn’t an easy one.

By Dr Alan Wager, Research Associate at The UK in a Changing Europe