I would actually recommend a serviced apartment in London. I did this for my parents when they came to visit me (I lived there 6 years). It came out cheaper than a hotel, more comfortable and better located than a hotel.

It had maid service and they saved major money by eating a lot of meals right there. Food in London is really expensive so it was nice to have a microwave, stove, etc. There are also a lot of small shops with ready-made food that's perfect for this set-up.

In case you're curious, they stayed in South Kensington, a very nice, yet still central neighborhood, partly because it wasn't far from where I lived. You may prefer something even more central but be wary of the noise issue. Also, many had a lot of stairs, which may or may not be an issue for you but do ask if that information is not available.

London hotels are infamously tiny. We're talking a tiny space around the bed so a rollaway is out of the question. The beds can also be small so get the exact sizes before booking.

This is a hotel chain that is "family friendly" and usually fits three to a room. We haven't stayed in one in London but have used them in many other cities;
http://www.novotel.com/gb/home/index.shtml

Normally, I would recommend Tripadvisor but I found that they don't have any means to find out which hotels are best for families.

Good luck!