Arch said:
The difference being, it's not illegal
Probably not illegal.
In his judgment in the Court of Appeal in Crank v Brooks, Waller LJ stated:
Waller said:
"In my judgment a person who is walking across a pedestrian crossing pushing a bicycle, having started on the pavement on one side on her feet and not on the bicycle, and going across pushing the bicycle with both feet on the ground so to speak is clearly a 'foot passenger'. If for example she had been using it as a scooter by having one foot on the pedal and pushing herself along, she would not have been a 'foot passenger'. But the fact that she had the bicycle in her hand and was walking does not create any difference from a case where she is walking without a bicycle in her hand."
Now I don't know all the facts of that case and haven't been able
to find the rest of the judgment on the 'net, but I would not be
surprised if "having started on the pavement on one side on her
feet and not on the bicycle" turned out to be a key part of it:
obviously someone walking along from A to B and pushing a bicycle
is engaged in a quite different form of travel from someone who
is cycling the same route and who only dismounts for the express
purpose of avoiding a restriction of some kind which is intended
to stop cyclists.