My mom was partially disabled so perhaps I notice this more than some, but just want to share a heads up that if you have mobility issues you will sadly have issues in London. Since many of the buildings are quite old, or are renovated versions of old buildings, the restroom situation is not ideal. You'll be climbing stairs in most cases either up or down a flight; I saw some locations that had added handicapped restrooms on their ground floor but I just took it for granted after a while that there would be stairs involved. And if you try to visit somewhere like the Chesire Cheese (or the Chuck E. Cheese as I took to calling it), it had one of the steepest and narrowest staircases I've seen in years, it would be tough enough for someone who had had only a half pint.
You'll also encounter issues in tube stations, especially if you're transferring lines. The walkways and tunnels are obviously original and not only can slope up and down but sometimes you think you're fine and then you'll encounter a small randomly located staircase. Again, this is just what happens with old construction but it's something to be aware of.