If you are not eligible for a wheelchair from the Wheelchair Service, or don't want to wait to be assessed by them, then you can considered privately hiring or buying a wheelchair yourself.
The Disability Living Foundation (DLF) provides a number of guides that can help you to choose the right wheelchair and other equipment, and give details of companies in the London area who hire out wheelchairs.
There are many websites which sell wheelchairs online. People First cannot recommend individual websites but has provided links below to some of the websites out there. We try to check all these sites for content, but cannot guarantee the content or links in any way. No items have been tested by People First and all information is provided without legal responsibility:-
Mobility equipment specialists: 
Businesses such as London Mobility, Fortuna Mobility,  Right Choice Mobility,  Adapt A Home and Wheel Freedom have showrooms in and around London where you can see and test products. 
And there are online businesses, some who may be able to provide video demonstrations:
Specialist rental companies: 
Companies like London Wheelchair Hire Ltd., Additional Aids Mobility, and Direct Mobility Hire offer short-term rentals with delivery and collection services. 
The Red Cross can also offer short-term loans of some kinds of wheelchair.