For clarity - there is no such thing as Right of Way in our traffic law - it is Priority - that may sound fussy, but there is a really important difference...
Right of way means that even if someone else is there first, you can overrule and ask them to get out of the way...
Priority means that you have first dibs on the area, but if the others (without priority) are there first they acquire that priority...
without that subtle difference it would be very difficult for our road systems to work - so priority is only used where there is otherwise a simultaneous clash...
in the Highway Code, the pedestrian has priority - however, had the car already been turning in before the pedestrian started to cross, then the car acquires priority - this means that the pedestrian can't throw themselves at a car which is already there, claim 'right of way' and blame the car...
so - all things considered, the pedestrian had priority as long as they were already in the road before the car started to turn (indicator is irrelevant, it is the point at which the car enters the road) - the driver is partially right in that the island can count as pavement as it splits the road, so being on the island at the point they turn in would not give the pedestrian priority - they are not halfway across the full road, they have not yet started to cross the second section of the road...
the OP's description is slightly confusing - in the first post they had 'just reached the island' - i.e. not passed over it and started to cross the next side... in the later post, they have already started to cross the next section... so I can understand the car driver's confusion...
however, if there were to be a court case on who had priority, then as the basis of law is that the pedestrian has priority, and with the pedestrian being the more vulnerable party, it would almost definitely go in favour of the pedestrian - generally speaking it is a responsibility for all drivers to avoid running over pedestrians :D
it is also though a responsibility for a pedestrian to look where they are going :)
so generally the outcome would be that the pedestrian probably has priority (depending on precise positioning), but car should have paused regardless / pedestrian should also have paused - and there should have been polite communication to decide who was going
i.e. technically - pedestrian is right - but morally, both are wrong :D