I know what you are thinking, let's go out and celebrate St Patrick's day since we are so close to Ireland. The trouble is you are in England and They are English and St Patrick is the patron saint of Ireland. So don't expect there to be much fuss over here for that. Also, it is not customary over here to pinch people if they are not wearing green so keep your fingers to yourself.
However London does have a parade which is free on the weekend closest to the holiday.