Peds!

through a sizeable segment stretch of my commute passing through fulham/chelsea, the entire cycle lane IS the door zone. it's pretty thin.
same thing with nearly all the CS routes which people can park in bits of.

Then don't ride on the cycle lane.

Just because it's there doesn't mean it's the safest and best position to be in, usually it's recommended to overtake the traffic rather than undertake to put less risk on yourself.

Even the highway code stated that you don't have to ride on the cycle lane if you don't feel comfortable on it.