I live in London and you see celebs on public transport sometimes.
I did think I might have seen Prince Harry on the Tube once. Years ago, before he had the beard. It was a young man with red hair, with a baseball cap pulled well down, so I couldn't see his face properly. I looked around to see if I could spot the Protection Officer, but couldn't, which I suppose is the idea.
I was with my mum in a railway station cafe in a city in the Midlands once. Peter O'Toole and another well known actor (I've forgotten who it was) were at another table. They were appearing in something at the theatre in that city. They were minding their own business and no-one was bothering them.