Eh, really? Interesting if the red light applies to the pavement alongside the road as well, never knew that.
Archaic, but true. Any form of transport with wheels is deemed in law to be a "carriage", as are animals used for transport - i.e. horses, but I suppose you could lump elephants and camels into that if you were being really anal.
If the letter of the law is taken at it's most pedantic, traffic signals (i.e. lights and/or authorised person giving hand signals) apply to carriages and animals in the roadway or on footways adjoining said roadway.
Strictly speaking, if you were driving a flock of sheep along a road and you come to a red traffic light or were told to stop by a copper, you have to!
I don't know how true it is, but I believe that the only time that you aren't legally obliged to stop at a red light is if it's temporary traffic lights or signals at roadworks. And also houses of ill repute, where it is inadvisable to stop at all if there are law enforcement officials in the immediate vicinity.
pushing a bike or pushchair you are still classed as a pedestrian.
But a pedestrian in charge of a carriage or conveyance - it is the carriage which must stop, not the pedestrian.
If you pick the carriage or canveyance up and carry it, it becomes a package and you can then proceed.