I'm OK. (What does that mean?)

Over coffee recently, a Chinese friend asked me: "Do you want cake with that?". To which I replied "I'm OK".

"That means you want cake, or you don't want cake?"

Fair point.

It means I don't want cake.

"I'm OK" in this context is a softer way of expressing no. I guess the root meaning is "I'm OK just as I am now" (so I don't need anything extra). I could also say something like: "Do you want another coffee, or are you OK?" - meaning, do you want extra coffee, or are you OK as you are now.

It is one of the many not-always-obvious colloquialisms in British English. Perfectly straightforward to other British English speakers. But not to somebody else trying to figure it out with logic!