It seems that five-year-old Alex was invited to the party during the Christmas break and his father said that he could come. The boy's mother later realized that Alex was scheduled to spend time with his grandparents on that same day and Alex said that he would prefer to do that. They didn't have contact information for the friend's parents, so they weren't able to send their regrets.
Once school resumed, the boy was send home with the £15.95 invoice. And Alex's parents are being threatened with going to small claims court.
I don't know how British courts work, but Judge Judy would throw the friend's mother out on her ear. There was no expectation that Alex would be responsible for a no-show fee -- verbally, in writing, or otherwise.
Needless to say, the boys aren't playing together these days. You should check out these email interactions between the two mothers at this link.