London's not as bad as people think. I've lived here all my life and only ever run in to trouble once, and I live in one of the worst parts of town. As long as you exercise common sense you'll be perfectly fine. Like Psy says, you should be more worried about pickpocketing than mugging, but neither is a particularly common occurrence.

Oh, and although it's a bit late now, you might want to try booking a ticket online for future trips, since you can get a much cheaper journey if you book a couple of weeks in advance.