Not all comprehensive policies cover driving another vehicle these days. It's no longer automatic. (My own policy used to include it then, when the broker found me a better deal with another company, I lost that cover. Now I've got it back again). Conversely, some third party policies do include it.
So, in terms of staying within the law, you're required to check that anyone who asks to test drive your car has appropriate cover. (If you fail to do so, and they get stopped by the police, you'll end up with 6 points on your own licence because permitting someone to drive without insurance carries the same penalties as actually doing so).
With regard to who would pay for any damage to your car, the same principles apply as to situations where no insurance cover exists or is required. If someone causes damage to another person's property, the owner of that property can demand compensation from the person who was at fault and, if necessary, take legal action against them to ensure that they receive that compensation.
So if someone test-driving your car is involved in an accident where the other driver is at fault, it would be that other driver (or, in practice, their insurer) who would have to compensate you. On the other hand, if the person driving your car was at fault, then he would be obliged to compensate you. The fact that there was no insurance cover for him (or you) to fall back upon would be irrelevant; it would be that driver personally whom you could demand compensation from (taking him to court to get it, if necessary)