Your insurer would have to prove that in having one of the tyres below the legal limit, that this led to the accident. The insurer is still liable for the third parties damage, though if you are in breach of the policy terms and conditions, it does allow them the opportunity to reclaim the third party losses from you. Make sure you control your asset. Get your car back or the insurer will undoubtedly try and sell it without your permission (I see this a lot). I would be arguing that the other three tyres were above the legal limit and as long as it had visible tread along three-quarters of the tyre and was not completely bald, that it did not cause the accident. I would advise them that it was soley down to driver error. Make sure you contest it, complain and escalate to the Financial Ombudsman service.