You're right, I should have talked about the Overton window more generally. But public usage of terminology is part of moving/spreading the window. It's quite apparent in the US discourse when very moderate politicians like US mainstream democrats are characterized as "radical left-wing extremists". Granted, there's a lot of hyperbolical "fascists" and "nazis" thrown around from the other side.

I find mainstream left of UK to be quite clearly center left. The current Labour government policy could be characterized even as center right.