Indeed, I don't think it's a coincidence that we're not really seeing outbreaks in London, when the tube is the perfect Covid spreading machine. The level of herd immunity in the big smoke may not yet be enough to allow full opening up, but I think you could open further without a major increase in cases.
London will be interesting to watch. Sadiq seemed to think it was about 3 days behind the curve, but thus far there has been no evidence of that at all - cases remain low. If anywhere in the UK has got anywhere near herd immunity, it will be London, I'd say.
What's quite interesting about cases now is that despite the very large local lockdown areas, it's very small specific areas that are affected - and the really badly affected ones are, as you might expect, those with lots of students! It certainly, if you look at a map, seems difficult to justify the Lancashire local lockdown's extent, as there are fairly large chunks of it with lowish cases.
That said, low cases doesn't necessarily mean herd immunity. Milton Keynes has had low cases throughout and continues to do so.