I'm another who says both share the blame.
In some ways I have more sympathy with the driver. If someone drove past a bike and left hooked in front of them, I would blame them 100%, but in this case it looks like the car is waiting for its path to become clear so it can turn left, and when it is clear the car proceeds slowly (although the footage is very short so that isn't certain). With a cycle path there, the driver should have made a final check before turning, but he might have done that and missed something in his blind spot. The car was indicating and the cyclist who was going too quick anyway, should have seen it and taken evasive action. As a cyclist, I would always be very cautious about filtering down the left hand side of a line of slow moving vehicles, especially where there are places to the left that those vehicles might turn into.
On the other hand, I have some sympathy with the cyclist, or cyclists in general. None of the comments question the suitability or design of the cycle lane, and like many other, probably most other cycle infrastructure, it is nothing more than a token marginal space on the left hand side of the road, that requires no thought or imagination, and does nothing to improve cyclists' safety. If anything, it reduces safety and the cyclist would have been better getting in the flow of traffic or filtering to the right of the slow moving vehicles, but then people would have been criticising him for being in the road and not in the cycle lane.
Typical Mail anti-cyclist mindset demonstrated by the totally irrelevant reference to the cyclist's headgear.