If his load was too heavy and it invalidates his insurance - you won't be able to claim from his insurance company, they will just walk away. Your only option then is to sue him privately, unless your own insurance includes cover for damage from uninsured drivers.
There is also a fund for claims against uninsured drivers through The Motor Insurers’ Bureau (MIB) - not Men in Black ! We all pay into this fund with a ~£30 a year levy on our insurance policies, so you and me pay for the "useless individuals" who drive without insurance. I think the excess is quite high for MIB claims £500+ ?? You will find details here https://www.mib.org.uk/
If your insurance company say he is not responding to them (as happened to me) call him direct and you may find they haven't bothered to chase him - find out who is handling his claim (the company and if poss the individual) and pass the details to your insurer