You actually highlight a pretty important point here. Cycle lane positioning varies so much in this country. How is anyone supposed to know where they are/when to look out for cyclists. In Brighton we have shared use pavements, the above mentioned promenade, by St Peter's church and the Level...
This. I personally always ride in the road round there. Until you get down to Hove Lawns, it is actually safer tangling with 1 ton metal boxes than oblivious pedestrians.
They should definitely suspend the cycle path by the i360 too, it is just too narrow for dual use now.