Billy Bunter was from the Greyfriars school stories by Frank Richards, which were published from about the 20s or 30s onwards. He wasn't originally the main character, just a comic relief figure, but he gradually took over the stories. He was pretty much exactly as shown (his catchphrase was "Yaroo") except that he didn't actually try to kill people
There was a TV version during the 60s, though I'm not sure it was on at exactly the same time as this story, so he was a very familiar figure.
Frank Richards wrote under a lot of different names (that wasn't his real one) and at one time was in the Guinness Book of Records as having written more published words than any other author on record. I don't know if that still stands.
How they ever got away with it is beyond me. Cyril even shouts 'yaroo' in the episode. It's so blatently Billy Bunter
