I don't have any legal qualification, but I have read the act (not just the highway code) and to the best of my recollection it applies only to vehicles. If you're walking on the road, no problem.
A bike while being ridden is a vehicle in law. A bike being wheeled - well, I don't know. If you look back before the bump you'll see the references to Crank vs Brooks where the judge ruled that a pedestrian pushing a bike across a crossing, who was a pedestrian before he started crossing and carried on being a pedestrian afterwards, was still a pedestrian. Some people will treat this as "a person pushing a bike across a crossing is a pedestrian no matter what they were doing immediately before or after", others might think that what the bike-pusher was doing before and after is relevant.
The intersteing thing, if it *is* legal to dismount just for crossing the line, is of course that you could legally remount just beyond the line and ride across the junction...