Congratulations on getting a nice trip like that!
I spent 3 weeks with my wife in the UK last year - including a whole week in London. Took heaps of shots and had my sling bag and camera with me almost the whole time. Harrods are a bit narky about bags on shoulders (you have to carry them - my sling bag was no bigger than a woman's hand bag but I got told off
), but everyone else was cool.
The only thing was to keep your eyes open for
no photography signs. Other than that - no problems at all.
Took shots in the Victoria & Albert Museum, the British Museum, the houses of parliament (where there are plenty of police) and around Oxford Street, Soho, Carnaby Street, Piccadilly Circus etc etc. If you get a chance, get a ticket to a live show (lots of ticket sellers around Piccadilly Circus and Leicester Square) - lots of great plays in London.
A week was no where near enough - and I've been to London a few times now.
Enjoy your trip!
Cheers