First off, chill. This isn't as big a deal as you might think, so don't stress.
To start with, you've had an accident, so you MUST report it to your insurer and/or declare it come renewal. Failure to do so may lead to your insurance being invalidated etc.
Now, the easy thing to do is just call your insurance co and let them sort it. I can't tell if you've done that or not yet. Legal cover is irrelevant, any injuries the TP may have will be covered by your standard insurance terms, so you already have enough cover for everything. Let them deal with it, any letters you get you can just pass on. That's the right way to do things.
On the other hand, if you're not going to tell your insurer at all, then Docwra's absolutely right. Pay him the £200, get him to sign a full & final settlement letter, and you're done. If he comes back later, you have that letter as proof that he was done with. You can then go to your insurer at that point if he really is an arse, however I suspect he's no intention of doing that.