Indeed, you are legally obliged to provide your insurance details to anyone who has a direct interest in an incident, so even if an accident is non-fault but the guilty party requests your insurance details, you must, by law, provide them.
It is easy to find out whether a vehicle is insured or not by logging onto www.askmid.com which is the motor insurance database on which all cars insured in the UK will be on.
Unfortunately, the fact that you are uninsured and should not even have been on the ******* road in the first place you complete and utter ****, does not absolve the other person - you will still, annoyingly, be able to claim from his insurers.