http://www.moneyclaim.gov.uk/
I would be inclined to accept that you both need a tougher fence.
If you really want your neighbour to share the cost or even pay for it all, you could write with a quote (explain that you are writing to keep a record in case court action becomes appropriate). You could be successful with a claim for compensation if there had been damage by the neighbour but, personally, I reckon that a football bouncing against it might count as general wear and tear.
Whether you fix the fence before claiming is up to you but you do need to put in writing what you are claiming and why you feel the neighbour should pay so that the neighbour has a chance to respond before you go to court.
My opinion is that, if you want a tougher fence more than your neighbour, you should pay. A claim for compensation would only pay for a fence similar to whatever you currently have,