"He's into me for fifty quid" means "He owes me fifty pounds". It's common enough in the UK, but I'm fairly sure I've heard it in American movies too (bucks or grand there, not quid, obviously), so I don't think it's particularly a UK expression.
But since I just had reason to say it, I got to wondering "Why 'into'?", and realised it's a bit odd. Is it just short for "in debt to"? When I say it, I feel like "into" is one word, and a quick Google shows that's how people write it, but if you just miss out the word "debt" you'd still have two words left.
Anyone know the origin/first use?