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London Fixed Gear and Single-Speed is a community of fixed gear and single-speed cyclists.
finger_jockey
Greenbank
[EDIT] I'm not sure what the crossing in question looks like, a google streeview pic or something similar would be useful if anyone can find one.
AIUI, you're propelling a vehicle (which includes cycling) which differentiates you from just being a pedestrian.
If you're propelling a vehicle then you must obey the relevant traffic signals with respect to stop lines. You can't just ignore them like you can as a pedestrian.
Whether getting off a bike and pushing it constitutes 'propelling a vehicle' is not clear, but the expectation is that it would. The only way to test this is if it went to court. And before anyone quotes Crank vs Brooks, that case isn't relevant here.
[EDIT] If this is crossing the road side-to-side on what would have been a toucan crossing (e.g. a green bike symbol), but it's a red signal, then I believe that's fine as you're not crossing a stop line on a red.