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My old man, now dead, told me many years ago that pushing a bike the wrong way up a one way street was illegal. I think he was talking specifically about during the war to avoid obstructing the pavement during air-raid running away drills. IF that was in fact true, bearing in mind he did have dementia, then it is feasible that at some stage "avoiding" a red by walking around it could also have been an offence. I can't see any cop bothering his/her arse to do anyone for it as long as no inconvenience is caused to anyone else.
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...