It means "how rude" in a light hearted manner. "Cheek" is meaning "cheeky"... as in "rude". It's what someone says in reaction to something they found mildly offensive :-) "how rude" is a more respectable way of saying it - "What a cheek" is a more 'common' way (slang). "What a" can be used before other things like "what a piss take" from the idiom "taking the piss". "Taking the piss" is an English (UK) expression meaning - that's an absolute joke (bad or stupid thing). e.g. You are waiting in a queue and somebody pushes in front of you... You say "what a cheek!". (usually to yourself or the person you are with but feel free to say it out loud ;-) ) I am from the UK and this is definitely the right answer (I hear it used all of the time) :-)

What a cheek! = What an example of impudence! I think it is an English UK phrase. Definitely never heard in the US

US - the saying is "What cheek!" (no "a") and it's something you would almost never hear. It doesn't mean "rude" as much as "audacious." It's a flashy, big, bold, and attention grabbing - that's on the edge of appropriate behavior or speech.