I think that it should be up to individual institutions to decide who can enter or not enter. No more government edicts, please. My "vaccine passport" is on my NHS app (to be clear, not the track-and-trace shambles which I deleted months ago). I'd be more than happy to show it if asked at the entrance to somewhere or other. I never have been asked for that, but I have been asked by two neurotic shopkeepers (out of all the dozens of shops I've been to since the great easing-up of July) to put on a mask as a condition of entry. The irony is that my unasked-about vaccinations are invaluable whereas the scruffy, ancient, just-in-case mask shoved in my cargo pants pocket* is almost certainly useless. But if it keeps them happy...

*As with most mask-shunning folk these days...