The police report you have is basically gold in this case, because it proves there was fault on the part of a third party and that it wasn't just an accident on your part. The insurer's denial based on "it wasn't a collision with another vehicle" is legally weak - most policies cover damage caused by third parties generically, and a cyclist is clearly a third party. What matters is whether you can prove their fault, and that's where the police report and the witness come in.
Before going straight to SUSEP (which they already mentioned), try this: send a registered letter with proof of receipt to the insurer explaining the whole situation in writing, attaching a copy of the police report, a photo of the witness confirming it (even if by email), and citing the articles in your policy that cover damage caused by third parties. Insurance companies often reconsider when they see things documented and formal - sometimes it's just an employee making a bad call on the first go. Give them a deadline like 15 days to respond.
If they still say no, then you go to SUSEP with this whole file. You need to be prepared for the insurer to try arguing that you can't prove the cyclist's fault despite the police report (which is weak, I agree), but with a witness you've got good odds. The important thing now is not to let this slide - the more time passes, the more evidence disappears and the less willing they'll be to cooperate.