The High Street Kensington is a pretty good place for shopping, if you're into that sort of thing. Be warned, though, that London is pretty damn expensive. There's an M&S there, so get some pajamas while you're there.
Be sure to have a cream tea at some point; they're just delectable. The best ones are in the countryside tea shops, but you can still get good ones in London.
Be sure to stuff like the changing of the guard, the Tower of London, Westminster Abbey, the London Eye,
St. Paul's Cathedral... ♡♡♡♡ it,
this'll likely be more help than me.