there are special sticks/crutches for people who cannot grip much.
basically you lean on your forearm, and there is a handle that you wrap your hand around for extra stability.
maybe if you could get those through community physio, it would help to support your claim, that you do not usual function of hands ?
i also recommend that you get advice from people used to filling in these claims.
good luck.
To think that London, or anywhere else for that matter, does not belong to any one demographic