Probably the most important event at yesterday's shadow cabinet was a presentation by Labour's campaigns director Niall Sookoo of polling that purported to show that "our support has fallen because we back a People's Vote" - according to a frontbencher.

The party's chairman Ian Lavery, who opposes Labour backing a Brexit referendum, was thrilled and crowed "I told you so", according to my source. The shadow foreign secretary Emily Thornberry, who backs a People's Vote, "ripped it to shreds".

Another source said: "There was a presentation to the shadow cabinet updating on the local election and the impact of support for a second referendum on our levels of support, including doorstep feedback".

This was "North Korean style polling", one Labour source told me - which gives you a sense of quite how split Labour's frontbench team are on how enthusiastically to promote a referendum.

According to my sources, Labour will still go ahead with backing the Kyle/Wilson pro-referendum amendment when it is finally put to a vote - probably next Monday, and certainly during the week. That amendment says MPs would vote for the PM's Brexit deal on the condition it is then subject to ratification in a referendum.

Labour are split over calls for a People's Vote. Credit: PA

Corbyn's backing for it has given hope to many Labour members that a People's Vote could yet happen.

But neither the Labour front bench or Peter Kyle and Phil Wilson expect to win backing for the amendment at this first attempt.

And whereas up to now laying the motion was supposed to be the start of a process, it is now widely feared that Jeremy Corbyn would see its defeat as settling the matter - so that he could move on to a different Brexit route.

Those close to Corbyn think he is travelling quite fast to throw the weight of Labour behind the soft form of Brexit known as Common Market 2.0, which is the brainchild of the Labour MP Stephen Kinnock and the half-in, half-out Tory MP Nick Boles.

They spent well over an hour with Corbyn and Labour's Brexit spokesman Keir Starmer yesterday, according to a source, and both seemed "engaged" in understanding more about Kinnock's and Boles's hybrid of single market membership and a customs arrangement.

Kinnock and Boles themselves are increasingly optimistic that their Brexit model is the only one that could command a majority in the Commons rapidly enough to avoid a hard Brexit - and are keen that EU negotiators view them as the route to save Brexit on a shortish timetable, via a modification of the so-called Political Declaration on the future relationship between the UK and EU.

Were Corbyn to throw Labour's weight behind Common Market 2.0, then perhaps only the Tory Party - and not Labour - would cleave in two, if that's the Brexit ultimately adopted by the UK.

That said, those Labour MPs who want a referendum would be (are) incandescent. So it's not inconceivable a few more of them would jump to TIG.