Naturally, the precise answer will vary according to the precise circumstances, and it goes without saying that specific advice will be required in specific cases, but here are some general observations.
When there's an accident which causes damage or injury to someone or something, the person flying the aircraft will be liable if personally at fault, but it is possible to conceive of a circumstance where the pilot will not be at fault. Take the case of a tailwheel falling off. Suppose that the pilot can show that he carefully checked the tailwheel assembly before flight, but, unbeknownst to him, there was a hiddden fault which led to the wheel falling off. Here, section 76 of the Civil Aviation Act 1982 kicks in (I append the text to the end of this posting). The owner has to stump up on account of the stunned cow, whilst the pilot laughs it off in the pub. Strict liability arises in respect of damage to persons, cows etc on the ground.
PS: I am sorrry that we sometimes snipe at each other in these discussions. We really ought to meet up, so that you could take me whizzing through clouds in your machine and I could take you upside down in mine (probably not a good idea if we try this in reverse).
s76(2) and (3) follows:-
Subject to subsection (3) below, where material loss or damage is caused to any person or property on land or water by, or by a person in, or an article, animal or person falling from, an aircraft while in flight, taking off or landing, then unless the loss or damage was caused or contributed to by the negligence of the person by whom it was suffered, damages in respect of the loss or damage shall be recoverable without proof of negligence or intention or other cause of action, as if the loss or damage had been caused by the wilful act, neglect, or default of the owner of the aircraft.
(3) Where material loss or damage is caused as aforesaid in circumstances in which—
(a) damages are recoverable in respect of the said loss or damage by virtue only of subsection (2) above, and
(b) a legal liability is created in some person other than the owner to pay damages in respect of the said loss or damage,
the owner shall be entitled to be indemnified by that other person against any claim in respect of the said loss or damage.