You could try demanding that the Highways Agency (if it was a major trunk route) or the County Council (for all other roads) pays you compensation for your loss.
If you do, the matter will be passed to their solicitor. He (or she) will examine the evidence to see whether it's likely that a court would rule in your favour. There are two main issues that would need to be considered:
Firstly, the solicitor would examine whether, based upon the balance of probabilities, a court would uphold your claim that the damage was caused by a pothole. You'd need to provide details of the location and measurements of the pothole (preferably with photographs including a ruler or measuring tape) and a mechanic's report stating that the damage was consistent with the vehicle striking a pothole.
Secondly, the solicitor would examine whether you could show (based upon the balance of probabilities) that the council (or Highways Agency) had been negligent. Potholes can develop in a fairly short time, in even the best-maintained of roads. No court would expect every council to examine every single inch of all their roads every day. To show that the council had been negligent you'd either have to show that large sections of the road were filled with potholes (indicating generally poor maintenance standards) or that the council were aware of the specific pothole and had failed to do anything about it (either by repairing it or coning off that part of the road).
Simply having a pothole in their road doesn't indicate that the council has been negligent. As stated, they can't be expected to examine every inch of their roads every day. If you can't show that the council (or Highway's Agency) has been negligent, any court action would be bound to fail. Their solicitor would tell them this and advise them not to pay out.
Chris