The slang/cant use of -er at the end of a word (or a slight modification of the word) was known as the "Oxford -er" so may well have its origins at the University. "Harry" is a euphemistic intensive, rather like "flipping", "ruddy" or "blooming" to avoid naughty words ..... which is why one doesn't hear many of them these days
I remember hearing "Harry Preggers" for pregnant in my youth, and I'm sure I've read "wagger pagger bagger" for wpb (waste paper basket) somewhere - Wodehouse maybe. And of course "rugger" and "soccer" have that origin too
I'll see if I can find reference for the "Oxford er"
[edited to add]
For once,
Wikipedia seems correct and informative....