It should be remembered that Corbyn's Halal-Labour (as opposed to Haram-Labour, whose members sometimes forget and call women 'love', support the home nation team but don't support transexual toilet access, and generally enjoy a fag, a pint and a quiet respect for Israel) is officially Brexit, much to the chagrin of many remainer members. If the recent council elections cemented, as pollster John Curtice remarked, May's party as the political host of the 'Leave' soul then it also highlighted Labour's split personality in trying to be the party of Leave and Remain simultaneously.
UKIP's voters, 4m direct electors at the party's peak and probably another 4m who held their noses and voted Dilettante-Conservative in 2010, have used the council elections to deliver a stark warning to CCHQ; you're the party of Leave, or you're finished. Polling analyst Rob Ford estimates 70% of Conservative voters are now Leavers compared to 30% of Labour voters, but that can't last.
Corbyn is under huge pressure now from the parliamentary party, Labour peers and the metropolitan strongholds to go fully Remoaner Halal-Labour, win back a drift of the Remain vote to the LibDems and cement the power that Labour failed to secure in the megacities on Thursday. The rump of Haram-Labour and cerebral Labour Leavers can find a home in the Conservatives. Right now, Kate Hoey is more of a Conservative than Anna Soubry.
Or so goes my theory. The trick for May's party will be to occupy both centre ground and Leave simultaneously - not as easy as it sounds. And there are nascent third parties forming in the wings and attracting attention from big-bucks funders that could be insurgent contenders in 2022.
However, I can see no longer-term downside (for us) to Labour abandoning Leave; a pure Halal-Labour will be powerful, run the large metropolii but will never be anything other than a strong opposition in Parliament. the Brexit process is screwed anyway and it will never happen cleanly - if it takes a decent majority in the 2022 parliament to make a clean break, we can live with it. We just need to be sure that May's team makes no agreement, no concessions, no treaty with the EU now that can't be reversed under a new administration.