The Police don't normally get involved in this type of thing at all!! Very strange-maybe he has a mate working in the station. It sounds like a fixed penalty notice and it may be time consuming and expensive to deal with yourself, but if you have legal protection on your insurance they may take it up for you, strange that he hasn't made a claim through his insurance company though, or you don't mention one, anyway.....
Time for a counter-attack:
When this chap asked you to get out of your car, was he in the remotest bit aggressive or threatening, in YOUR consideration?
if so, immediately report it to the Police- preferably the same station your letter came from, they will be duty bound to investigate it.