I didn't see any mention of it (could have missed it),but are you running run flat tyres?
Hitting a pothole can certainly crack the wheels,especially the bone china 225's!
The probability of cracking is magnified if the tyres are runflats,the walls of the tyres are rock hard,more so when it's cold,the tyres won't take any shock,so it's left to the wheel to take it,hence the chance of cracking.
The only fail safe way of checking the wheels for cracking, is to either take the wheels off,or put the car up on a lift,the hairline cracks are very difficult to see when lying under the car especially if the wheels are dirty.
It could be that one,or two of the tyres has blistered which would cause the symptoms you describe,especially the vibrations through the s/wheel,if that is the case,it will only get worse,and in extreme circumstances the tyre will implode.
Find a decent tyre specialist,and ask them to pop it up on a lift,if the wheels are cracked it will then be evident.
It you are thinking of claiming from the council,you'll need photographic evidence,detailing width,length and depth of the pothole,the more detailed the better,Council's are notorious for kicking out claims,but prove the case,and they will pay out.
Good luck,with all of it