Yes you can claim this increase from the other party's insurer. You'll be advised that you cannot, but that's because solicitors are not used to claiming it back. You need to contact your legal assistance provider, or a solicitor, for 'uninsured loss recovery' and claim for the next five years. I think it's a scam that insurers penalise you for an incident that isn't your fault, and then not expect you to claim it back from the at fault party.