I know of no part of the pavement on Devonshire Road that is wider than the sections of Honor Oak Park where pavement parking is permitted. So why is it ok on Devonshire but not on HOP?

Times have changed indeed. In London, since the 1990's there has been a steady shift from private to public transport. See here for background:
http://www.tfl.gov.uk/assets/downloads/c...port-1.pdf

I'm not being anti-car here, I accept that residents need parking spaces. I just don't think that pavement space should be restricted to ease the passage of cars - this would seem to be running against the trend.

My own experiences of not being able to get a pushchair past parked cars on a DR pavement was with a pushchair. Not a Silver Cross pram, or somesuch, which one might envisage when you refer to "massive prams"