I always assumed it was from the Latin phrase Quid pro quo. The phrase itself means ‘something for something’, so definitely makes sense in context.
Quid is used as a plural. I find it much easier to say ‘fifty quid’ than ‘fifty pounds’. But then, not all slang is necessarily shorter. See Cockney rhyming slang.
I’m pretty sure the Quidhampton thing is a joke, btw. Some sites claim that the Royal Mint was once located there, but AFAIK it has only ever been sited in London or South Wales, near Cardiff, its present location. I can find no evidence of there ever being a paper mill in Quidhampton. Not that bank notes are actually made of paper, of course.
OK, apparently there is another Quidhampton in Hampshire, not far from a place called Laverstoke, where bank notes were indeed manufactured. But since other larger and more well-known towns such as Whitchurch and Overton are nearer to Laverstoke, it seems unlikely that an obscure village such as Quidhampton would be associated with the bank notes.
Pound sterling is also known as ‘nicker’, which is two syllables. I believe it may be more popular slang in the north of England, but I can’t be certain. Don’t have a clue what the etymology of that could be.
Maybe it’s Quid Pro Quo because that’s what the real pros charged.
There’s the joke that when the current one pound coin was introduced, they said it should be called a “thatcher” - because it’s thick and brassy and thinks its a sovereign.
Yes, it was a shilling. Shillings don’t exist any more, of course, but people might still say “bob” sometimes. It provides a chance to confuse the younger people and it sounds more satisfying if, for instance, complaining about the price of things these days.
And an old sixpence was a “tanner” but I don’t know where that came from.