Yes, relevant back story would have been clever and useful.
We're all most likely aware that only having one leg has quite an impact on anybody's life.
But on the basis of the narrative presented to the viewer, we have a man who can afford offices in central London, pay for a secretary whether he has work or not, have a good old drink etc etc - - simply put, he is not portrayed as hard up.
But a one-legged man who chooses top floor offices with no lift in the most expensive part of London and then walks everywhere, is obviously making a point? or is a badly drawn character.
Otherwise, he would have a ground floor office with a parking space and a mobilty allowance in Peckham or Bromley.
Sometimes writers labour too hard to be different, pretentious names, overworked back stories etc etc - sometimes simple is just better