Getting around London in a wheelchair is hard, not all roads have ramps, and a lot of the ramps are so badly made, we have had to lift the wheelchair most times anyway, and that's if some car is not blocking the ramp! London is not known to be access friendly, or stiletto friendly for that matter, especially through cobbled roads.
Advance planning is the key to a convenient time around the city when you need special access. Google Earth is a great tool to see the actual place you're going to so you can go check for visible ramps and various access, see if there are steps. I can manage to walk a bit, seeing the place ahead gives me an idea if I can handle the walk and leave the wheelchair. When booking an attraction, check the website for access information, if there isn't any, call ahead and ask. At Madame Tussaud's for instance, you are required to book ahead as they limit the number of wheelchairs per hour, and understandably so, it gets crowded and navigating the exhibit an inconvenience. Use your cancer perks, if they offer anything that would make it easier for you and your family, take it! Disabled people and their carers can go in free at some attractions where viewing is otherwise limited and not accessible for wheelchairs. London is an old city, fitting my wheelchair into old small lifts posed some problems for us. The best part is, in most attractions, you actually jump the queue. During our cruise, I decided not to take my chair, and we regretted we didn't as we could have gotten the best seats and skipped the lines. At Buckingham Palace, the kids were thrilled that we entered through the front gates and saw up close the royal guards, not everyone gets that. Eating out presents its own set of predicaments, for one, most restaurants in London have their toilets a floor below or above the restaurant with no lifts, very few disabled toilet facilities unless you stick to malls. I can manage a few flight of stairs but I can imagine the hassle for someone who can't walk at all. I thought London would be a pioneer in Vegan cuisine but I find that not to be the case, unless of course you specifically go to the specialty restaurants which you can't do every time especially when you're touring with kids. Most restaurants idea of a vegan meal is dumping cheese on vegetables like cheese would just make it gourmet. The wheelchair can be folded and fits into a car and taxi easily and most drivers help you get settled, there is no need to call ahead for a special ride. The other challenge with getting out and about is dealing with crowds, with a low immune system like mine, I have to protect myself from catching anything, wild events like concerts - not a good idea!
Plan ahead, know the venue, ask for help.