Hi, even if the owners have a sign to say as Maccluff's answer they have a duty to maintain the car park, If the land / car park is owned by the Parish Council them are the people who deal with the claims, Take photos of the offending pot holes, measure the depth / width, (No I am not joking) Time / date / your damage to your car, the cost of repair, the quote from the repairing garage get all your fact before you put in your claim. I have just been paid out by Network Rail due to a crossing in our local town been in a disgusting state of repair, do not back down fight your case.