Yeah, some of those designs look pretty bad. The solution in London at busy intersections is to have separate signals for cyclists and turning motor traffic. Turning traffic will have a red light while cycle traffic has green and vice-versa.
At smaller intersections without signals, the turning motorist is responsible for looking for (and giving way to) cycle traffic before turning across the cycle lane.
As a cycle commuter I feel like London compromises very heavily because the authorities aren't willing to reallocate or expand the existing road space to do what's necessary, and instead just do what they can.
True. It's much better than it was 5-10 years ago, but there's still much more to be done. Some councils are better than others.
Obviously most London roads can't be "expanded", but even reallocating a few parking spaces can often create a lot of space for cyclists and pedestrians.
I'm obviously biased as I commute 18 miles from South London, but I think it could be done. We built tarmac roads where they didn't previously exist, after all.
I think the core problem is that councils are allowed to drag their feet or do dumb shit. CS3 is too narrow to safely passage oncoming traffic and veers across roads, CS7 has a "safety" bollard right after a chicane. These don't seem like the actions of people who view separated cycling infrastructure as a priority.
At smaller intersections without signals, the turning motorist is responsible for looking for (and giving way to) cycle traffic before turning across the cycle lane.