I spent a month in London by myself when I was 21. Never once felt unsafe. Splurged on taxis a few times after leaving clubs really, really late at night but otherwise just followed the locals' lead and took the tube pretty much everywhere, any time.
Heed the usual precautions to keep alert of your surrounding and you'll be fine.
Originally Posted by
Analise
No one can tell you that you're taking too much time at the Tate.

That's no lie! ^