Strictly speaking you have to report it to a constable as soon as is practicable, or in any case within 24 hours, or simply within 24hrs dependent on the nature of the incident.
That said most station front desks won't have seen a police officer since the 80. I got my own station in 2007, a big one too, and that came equipped with two - very good, it has to be said - civilian lasses on the front counter, so reporting it to a constable is tricky.
I've been out some years now but expect most take a fairly relaxed view so long as it is actually reported and would want you to report it online these days. Which is fine if you're not in your 80s like my old Dad, who would rather have the clap than the internet.
The police will not tell your insurers you've been in a prang. There is no legitimate policing purpose in doing so, so to share such information would be unlawful under DPA, our domestic interpretation of GDPR into UK law.