Agree with your first sentence but he is described as being on the very left wing of the party and, if he becomes PM, it will be with the support of the left wing, not the blairites.

Then we will have a hot-minute before they're utterly hating him and demanding he goes too

> he is described as being on the very left wing of the party

By whom, and why are they worth taking seriously? Some politicians these days say all kinds of deranged nonsense about their opponents, and very often paint them as "far left" regardless of actual position. It's not worth taking at face value if it comes from there.