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Don't want to get into the armchair lawyering (especially with a lawyer) but isn't that covered by the full wording of s72 of the Highway Act 1835:-
“If any person shall wilfully ride upon any footpath or causeway by the side of any road made or set apart for the use or accommodation of foot passengers; or shall wilfully lead or drive any horse, ass, sheep, mule, swine, or cattle or carriage of any description, or any truck or sledge, upon any such footpath or causeway; or shall tether any horse, ass, mule, swine, or cattle, on any highway, so as to suffer or permit the tethered animal to be thereon.”
One would assume that riding a bike is covered by either the 'ride' part or the 'drive' part of the second clause. But pushing a bike along the footway is neither 'ride', 'drive' or 'lead'.
The law for red lights and stop lines specifically mentions 'propel a vehicle' over the stop line, but s72 of the Highway Act doesn't use 'propel'.
Greenbank-
If walking over a stop line with a bike constitutes 'propelling' it across the stop line, then I don't think it's stretching the usual use of language to describe walking a bike down the pavement as leading it on the footpath. But as you say, until there's a decision on the point (which there probably never will be) it's all a matter of opinion. And as, we all know, opinions are like arseholes.
Brommers
Follow that logic, however, and it's hard to see why pushing your bike wouldn't also fall within the term 'lead or drive any horse, ass, sheep, mule, swine, or cattle or carriage of any description' given that a bike is a carriage. And if that's the case then it's illegal to push your bike along the pavement...