Rights or wrongs of who should have stopped or who had right of way, the driver should be claiming through her insurance.
Who called for an ambulance? Who required the ambulance? You or the driver? Were the police notified? There are implications way beyond whether you have to pay for the damage to the car. Insist that the claim is made through her insurers and check your household policy for your own level of cover/liability.
And talk to citizens' advice.
Sketch out the accident (honestly) - by returning to the scene - and prepare a written statement - be prepared for the insurance claim even think what your evidence would be if the driver took you to court.
As a cyclist, I witnessed a bus side-swiping a car a couple of years ago. The case went to court where it was accepted that the car driver probably went through lights on red but the bus driver was found to be at greater fault because he couldn't describe the road junction or the sequence of the traffic lights (even though it was his regular route). The council put screens over the lights just after the court case as there was a pedestrian crossing light that was clearly showing green much brighter than the red traffic light - but we wouldn't have known that if I hadn't gone back and made a sketch and noted the sequence of the lights from all directions. It was just luck that there hadn't been a fatal accident at the junction