All London's crossings, which tourists are more likely to be familiar with, are Pelicans, although sometimes modified with countdown timers in busy areas.
London doesn't use Puffins by policy, I'm not sure exactly why - in very high density areas I can see that the Puffin features aren't helpful, but that doesn't explain a full policy.
[Differences: A Puffin's cross/ don't cross indication is local, your side of the road, next to the button and angled such that you're looking at oncoming nearside traffic as well as the indicator; whereas a Pelican has indication atop a post on the far side of the road. The timers work differently meaning Puffins can react faster if unused for a period and then called, initiating a walk cycle very quickly in this case if able; if you're road traffic the difference is that Pelicans use flashing amber and Puffins never do IIRC]
There are definitely puffin crossings in London. But I think you're right - central London tends to have pelicans. The policy must not apply throughout greater London though.
Sometimes in the west end you'll have a hundred people waiting to cross - higher pedestrian signals on the other side of the road are probably more visible to everyone in that situation. And I guess it's helpful if crossings are consistent in an area: particularly in areas with lots of visitors.
To be fair, if huge numbers of people want to cross, it's actually mere politeness which keeps them from just doing it. If you just walk into a busy street, you'd perhaps be hit by a car and injured or killed, but, if a hundred people do it the cars are forced to stop by the literal weight of the obstacles.
I remember thinking about this on my way back from a London fireworks display (Richmond maybe? Somewhere that way) because obviously an entire crowd of thousands want to cross a street suddenly and they're not going to politely queue up and wait for light changes, they just all cross, because there's nothing car drivers can do about it. A few minutes away, with the crowds dispersed, it was necessary to actually use crossings, but outside the park where thousands of people had just watched the display a crossing was completely superfluous.
