Surely for London the answer is the deepest underground station/line you can get to in the time given?
I live and work in or very near the centre of Bristol so I'm not sure of the danger. North Bristol's factories might get hit (Airbus, Rolls Royce) which are only a few miles away but otherwise not sure what strategic targets there would be other than human. There is a basement at work but doubt that'd do much. There's also some caves under the centre and tunnels under Temple Meads which could be a good bet if they were opened up in this scenario but you'd be stuck down there for some time. Otherwise cycle as fast as I could south into Somerset if I had maybe half an hour plus.
Nitefly, as a fellow Bristolian, where would you go?