If you're planning to stay in the London area, I recommend contacting Dolors.
While her place isn't in the direct center of the tourist area, it's a very quick tube ride away - with a tube station just two blocks from her apartment, and the famed Abbey Road just a few blocks in the other direction! The title of this space is also very well-named, the view from your room cannot be beat at 15 stories up above the town.
Dolors is a very respectful host and leaves you to your travels as you come in and out of the house, while also making sure you have everything you need.
The unit itself is secured behind a building entryway lock and the unit's individual door lock, so your luggage is insanely secure.
If you're looking for a good spot to crash, this is it!