Apologies for the delay in responding, I had gone off to watch a very damp firework display and have just about dried out!
It is the responsibility of the owner to ensure that there is at least the minimum liability cover in force for the operation of the aircraft. Thus if he allows you to use the aircraft as part of its normal operation then you, or your estate, would have the protection of the owners insurance cover for damages awarded to an injured third party, or their estate, at least to the limit of their cover.
Where it gets tricky is if the owner has only arranged the minimum cover and the value of the damages exceeds this. That is why it is worth making sure that the insurer has a decent limit of liability on their policy, not just the minimum.
Also check if they have arranged cover as a ‘combined single limit’ which helps ensure a better level of cover specifically for passenger liability. It still terrifies me that there are a lot of private owners out there with only a £150k odd cover per passenger for liability which would not even scratch the legal fees in the event of a serious injury claim. This is not just an excuse to generate more premium as increasing liability cover, especially on a CSL, is not that expensive.