There's been a bit more work going on at Chelsea Bridge for Cycle Superhighway 8. Let's see what the TfL elves have been doing:
Below: It's still difficult to filter on the outside because the island restricts access to the advance stop box. However, you don't want to stay on the outside because you're on the wrong side of the motors to get into the cycle lane on Grosvenor Road. The best plan may be to try to cut in between the two lanes but that can be tricky to achieve and may be dangerous if the lights change on you at an inopportune time.
Below: they've added a cycle reservoir in the middle of the junction where you can wait to make the turn into Grosvenor Road. I'm not very convinced by this. For a start, it's too small, and it's too narrow at the front, just when faster cyclists will be overtaking slower cyclists.
These are all improvements, but they don't address the fundamental problem of how to get into advance stop box and get into a good position for the right turn. Cyclist are being forced into dangerous positions on the road for no good reason. It is not beyond the wit of man to design a junction that is more cycle-friendly than this one, and given that this is a critical junction on London's newest and most expensive cycle facility, there really is no excuse for getting it wrong. If this is the best TfL's engineers can do, they need to quit and let somebody else (perhaps somebody Dutch) have a go.