It's a common myth that insurance is voided by other illigalities. If that where the case every prosecution of any sort would be accompanied by one for no insurance. Clearly a nonsense. What it means though is that by not having tax for example, you are giving your insurer a reason to refuse or reduce your claim. They will generally still cover third party risks. They may well seek to recover third party payouts from you if you are seriously illigal. For example if you are drink driving and cause an accident they will probably pay third party damage and sue you for it. etc etc