The new chapter Getting Around 2013 includes comprehensive information about getting around by car, taxi, bus, rail and tube with some helpful tips about how to make the best use of the system and when not to travel (if possible). There are 59 pages covering the system as it is now, together with plans for improvements up to about 2020 (such as the opening of Crossrail).
Getting around has become somewhat easier during the past few years, but there are still some significant challenges.
There’s an excellent RADAR write-up which you can download, called Doing-Transport-Differently, which may have some useful ideas for you. It is not just about London.
In the magazine Disabled Motoring UK, Oct 2014, page 14, Edward Donohoes highlighted some limitations of the new bigger Mercedes Taxis. Although some of the cabin dimensions are bigger that the traditional TX versions, the Mercedes has some problems in accommodating larger electric wheelchairs. Also it does not have a seat which swivels out over the pavement (which is particularly useful for some). The Mercedes is higher off the ground than the TXs, and has less height in the cabin. A chair user may finish up lowering their head towards their chest.