//...erm - dont listen to that one//
You should listen.
There are two aspects to motor insurance: firstly the Third Party cover required by law and secondly the remainder of the "Comprehensive" cover which most policies provide - cover for fire, theft and damage to the policyholder's own vehicle.
As far as the first, there are very, very few reasons why an insurer can repudiate liability for third party cover - and having no working odometer is certainly not one of them.
Their responsibilities for the second are not quite so onerous and they can reduce or decline payment for more reasons, including defects in the car. However, they will have to show that the defect either had a material effect on the reason a claim is made (e.g. faulty brakes causing an accident) or that it had a significant effect on the insurer's risk - and hence the premium paid (e.g. the vehicle having non-standard modifications which influenced performance).
They would struggle to do either for a non-working odometer. Yes, it may be difficult for the policyholder to prove the mileage of the vehicle, but that would not be a reason by itself to reduce a payment.