If you're looking for things to do during your 10 days alone, the UK&Ireland forum gets asked that question a lot & has some fabulous suggestions. Not just the main tourist places like the V&A, but smaller museums, restaurants, libraries, etc. They also get asked a lot where to stay in London. So if I were you I'd wander over to that forum & look at the various threads there.

I'd be stunned if you picked a lowlife area in London to visit or stay at, so I'd say take the normal precautions you would with any city in the US or world & you'll be fine. I'm in London a lot & I don't want to say the safety thing doesn't cross my mind, but I've never been somewhere I didn't feel safe, even late at night.

Cheers.