Sorry you don't seem to. It looks like you've checked some waffle on gov.uk that is their advice but not the law.
not having made any pretence at saying "I know the law". You wish to say that, fine. Just don't mislead people into thinking that you "know the law" any better than anyone else.
"Press and wait for the green figure to show, another way of saying stop?
That's just their advice. I know the law on this one.
Traffic Signs Regulations and General Directions 2016 SCHEDULE 14 PART 1 Paragraph 9 "(3) The significance of a red symbol when illuminated is that, in the interests of safety, pedestrian, equestrian or cyclist traffic (as the case may be) should not use the crossing" and there is currently no offence of using it, or of passing the toucan or puffin red symbol, or more generally of "jaywalking" (jayriding?).
It's probably slightly safer to wait patiently minutes for the green symbol (due to a slightly higher probability of misjudging an approaching vehicle's speed or direction than of being hit by a pavement driver while you wait, or a red light jumper when you cross) but it would be a farking irritating life spending so long each trip giving way to empty space mainly because whoever programmed the lights gave more green time to motorists than humans.
So, if we want to get somewhere faster than that, riding on the carriageway would be faster because it's more likely to get green at some of these stupid lights and is perfectly legal and also fits with all official advice, but that means merging onto the carriageway before the lights (one of the top ten most hazardous moves for cyclists) and riding amongst high-speed motorists whose attention is on their lights, not you, with many of them behind you where you can't see them easily.
So I think that's less safe than treating puffin reds as give-ways, which is perfectly legal but ignores some advice. In the vanishingly unlikely case that I get splatted on a junction in a way that I would not if I'd been on the carriageway, you can say "I told you so". I'm still not going to waste my all-too-limited remaining time on this planet giving way to fresh air because British traffic lights are crap, any more than legally required!