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The collision appears to have happen, from the position of the car just beyond where the lollypop lady is.
HousecatHST-
Hmm, that crossing is further from the junction than I expected. I'm assuming (from your description) the cyclist was coming from left to right as that streetview link shows.
To answer your original question: No, I don't see how any cyclist could read that they have any form of priority to cross that junction to the shared use path on the far side. There just isn't the signage or road markings to indicate that.
That being said...
If the car was turning right they've just come from a 40mph limit into a 30mph limit and sight lines may have been obscured by non-turning traffic in the opposite lane. If they weren't able to see they should be appropriately cautious. If they were taking the corner too fast then they're a twat.
If the car was turning left they've been in a 30mph limit for a while and sight lines should have been good.
Given the distance of the crossing from the junction, you would assume that a car turning in (from either direction) at an appropriate speed should have had plenty of time to see someone still crossing and to slow down or stop in order to let them finish crossing.
So, in most likelihood, it's a going to be a vast majority of the fault of the motorist.
The only thing that would start to shift some of the blame onto the cyclist would require knowledge of the speed of impact of the car and the point of impact on the bicycle.
If the car is doing ~20mph (or more) at this point then there can be little argument that that kind of speed is inappropriate at that point (although this doesn't mean they're entirely at fault).
However, if the car was going 20mph or under and only just clipped the front wheel of the bike then it would say to me that the cyclist knowingly started to try and cross the road even with the car approaching.
If the car was going 20mph or under and just clipped the rear wheel of the bike, then it's 100% the fault of the driver. There's too much distance and time not to have seen the cyclist that was already most of the way across and slowed down accordingly.
In between those two extremes you've got the blame accumulating for one side over the other with the benefit of the doubt going to the person crossing the road as the onus should be on the motorist to expect the unexpected and be in a position to stop.
Greenbank
HWC Rule 170: http://www.highwaycode.info/rule/170
I don't think that is of any help here. The cyclist, by cycling at the time, isn't a pedestrian.[1]
I'd need to see a picture of the junction (is Streetview accurate, if so post a link) to say any more.
From the description I would hope that common sense would put the vast majority of the onus on the vehicle turning, but sadly I can guess how this will end up playing out.