You have 3rd party cover so problem solved in this instance.
Wait for him to contact you requesting your insurance details and then give him your third party insurance details.
That, in theory, should be the end of it.
You will no doubt be contacted by your insurance provider after he submits his claim but that will be for verification of the circumstances as alleged by him.
Sort of off topic (sorry), but I'm reminded of an incident I had ages ago.
Had a nasty note from a solicitor, claiming I was at fault in a RTA. I wrote to CTC's legal thingy, giving details (the other parties' claims were largely lies. I had witnesses, and police/ambulance reports would have confirmed).
Never heard anything again. Standard practise?