A few words of caution:
The council will only be liable to pay compensation if you can prove NEGLIGENCE on their part. If they reject your claim (and you pursue it through legal action) you will need to show either that the council's system for checking for the presence of potholes was inadequate (i.e. they never really bothered to check that the road was in a decent condition) or that they knew about the pothole but failed to deal with the problem within a reasonable period of time.
As an analogy, let's assume that you suffered an injury after slipping on a spillage in a supermarket. If you could show that the supermarket did not have any systems in place for spotting, and dealing with, such spillages you could get compensation. Similarly, if you could show that the supermarket was aware of the spillage but didn't respond fast enough to prevent your injury, you would have the right to receive compensation. But if the supermarket could show (perhaps through its CCTV coverage) that the spillage occurred less than a minute before you slipped you would not be able to get compensation because a court would almost certainly rule that it was unreasonable to expect a store to respond instantaneously to every spillage.
If the pot hole had only recently appeared, you've probably got little or no chance of a successful claim.