I learned two fascinating things about the Labour and Tory refuseniks in The Independent Group from my guests on the Peston show last night (at 11.05 on ITV) - though quite how much of it made it on to the show I am not sure, because we had a hard stop at the end of a jam-packed episode.

First Gavin Shuker told me that he and Chuka Umunna and other MPs still in the Labour Party made an offer to the PM after she lost the meaningful Brexit vote in January that they would support her in office for at least a year and vote for her Brexit deal if she pledged to put that deal to the people in a referendum.

Apparently the de facto deputy PM David Lidington and the chancellor Philip Hammond seemed warmer to this idea than the PM.

But Heidi Allen, one of the Tory defectors, told me - only half jokingly - that the 11 MPs in The Independence Group would offer their own confidence and supply arrangement to the PM, to replace the semi-estranged 10 Northern Ireland MPs of the DUP and allow her to govern, if she went for just that plan to put her Brexit proposal to the people.

And by the way the PM can trust The Independence Group to keep her in office. Because, as Allen confirmed, the last thing they want is an election in the next year - because they are a million miles from being a proper party with policies and an institutional structure.

So maybe the Kyle/Wilson amendment - which links support for a Brexit deal to a government commitment to hold a public vote on it - will be helped by the Labour and Tory defections.

Except that - also on the show - the ERG Tory Brexiter MP Maria Caulfield confirmed that the PM would lose the support of many tens of her own Brexiter MPs were she to endorse a referendum.

So we are back where we always were: if Corbyn backs Kyle/Wilson it may happen. If he doesn’t - even though Starmer, Watson, and even seemingly McDonnell have signalled they want him to - the referendum is dead.

Robert Peston is ITV's Political Editor. This article originally appeared on his Facebook page.