Can I claim compensation for a cycling accident if I did not get the drivers details?

[Jamie]

I was in a cycling accident that was not my fault, I was hit from the side by car while riding in the cycle lane and knocked me off my bike, they didn’t stop to see if I was alright and I didn’t get any details, can I still claim?
I went to hospital in an ambulance and the doctors told me x rays showed I had fractured my elbow, how much compensation could I be entitled to?