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Crossing a stop line at a red light whilst "propelling a vehicle" is the offence. Doesn't matter if you're considered a "foot passenger" thanks to Crank vs Brooks (the famous case you are probably thinking of), you're still "propelling a vehicle". Crossing a pedestrian crossing whilst pushing a bike isn't illegal because there's no wording in the law preventing people from "propelling a vehicle" across the road using the crossing.
Walking off the side of the road before the stop line and using a pedestrian crossing looks ok according to a vague reading of the law.
Who knows about other such fun as dismounting the bike, mounting the pavement, pushing a bike past the stop line and then rejoining the road before cycling off across a junction. Probably various careless/inconsiderate cycling offences the Police could play with there.
I'm a master of the graceful dismount and stroll along with the green man phase on the side road (i.e crossing as a pedestrian with my 'legitimate accompaniment', or whatever the ruling was in that famous case in 1981 ) before a classic scoot and remount on the other side.
I'd never RLJ but there are occasions at lights on quiet roads where you've just missed the green to go straight on and you know the phase of the lights off by heart where I think it's perfectly acceptable.
If I walk my bike onto the pavement, walk it across the green man phase, walk it onto the road the other side, mount and ride off, what possible law am i breaking (apart from in some peoples' eyes being a bit of a twit)?