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The incident was the drivers fault;
Maybe a very small percentage, but the majority of the fault is yours for not anticipating it and being too close to your mate when he hit the brakes.
I reckon you'd have no chance of making any kind of a claim against the driver (or your mate).
Look at it another way and take the car out of the equation; if you'd been riding behind your mate and his chain had jumped off the sprocket and locked up his rear wheel, and you'd ridden into the back of him, who's fault is it?
This morning I crashed out, I rode into the back of another cyclist (my mate) who had braked hard on seeing a car pull out from a residential side street to turn right into a static queue of traffic.
Basically I don't know what to do, if I can do anything at all. The incident was the drivers fault; they shouldn't have pulled out with two cyclists approaching at ~20mph, BUT neither of us hit the car. Ideally I'd like to claim and replace the wheel and shifter (could be more) that are knackered now, posting here to ask if I have a chance of that?