To be fair to them, that could genuinely have looked like you put the belt on after you saw them, and they're used to people giving feeble excuses. Not that yours was, but you know what I mean.
Sadly, some you win and some you lose in life. This time they were wrong, but there's precious little you can do about it. I wouldn't even bother trying to argue in court, not for the sake of £100.
You have my sympathies.