Plus one to this.
I'm afraid I have little confidence in the police - particularly traffic police - to investigate incidents involving cyclists. My experience, and that of many others I've talked to, they can't be arsed to investigate unless someone is killed - and even then it will be a cursory investigation with every benefit of the doubt being given to the motorist.
When I was hit and seriously injured the police took 45 minutes to turn up and then couldn't even be bothered to fill out the Incident Book correctly. They didn't note down the details of the three witnesses who had waited to speak to them and, further down the line, denied there were any witnesses. This led one of the witnesses, who happened to be a High Court judge, to have words in ears and I got an apology for their behaviour - but others aren't always so lucky as I was. When the police said there were no witnesses, the driver changed his story and his insurers then tried to deny the claim. It was only after the judge had intervened with the police and they were forced to change their story that the insurers accepted liability.