<inserts standard response>
Tbh when I'm driving I'm far happier when a cyclist jumps the lights ahead of me; I can see what they're doing, they're not right next to my car or right in front of it... I'm pretty good with mirror checks, but cyclists are silent and often surprisingly hard to see from a vehicle, especially if they're on the passenger side. Dangerously unpredictable too, some wait for you to move off, some have slower reactions so you think this is what they're doing, some leap off but wobble as they bring the bike under control etc.
As a cyclist I will always stop at reds until I know the way the lights work... Even then I always slow and check for peds and any other obstacles. Never skip lights when it's green for traffic crossing my path unless it's obvious there's nothing coming. Tbh many London roads have very good visibility and are often all but empty, I mean we cross roads like this all the time on foot and think nothing of it, for me it's similar on a bike. I cycled through central London nearly every day for 6 years including a 6 month stint as a courier and not once have I come close to hitting a pedestrian. It's just a matter of riding sensibly; if you see people on the pavements, slow down and make sure you know what they're doing before you attempt anything that might infringe their right of way.
I see a hell of a lot of idiots mind you, which is why I don't think I'd go for much change in the regulations... I have a lot of experience cycling in London, but many people don't and that kills them. It's like the lorry thing, the deaths that are being countered by the new EU mirror regs are tragic, but it's one of the first things I learned... Never undertake a lorry. In fact, IIRC, they brought one round to my primary school so we could see how hard it was for them to see us. Need more training like that for adults.