What it means
A proper screw-up or blunder where you’ve made a total mess of something, usually by accident and usually owned with a wince. You’ll hear it as a confession, like I made a right cock-up of that, meaning it’s all gone pear-shaped and the blame’s on you. Similar to balls-up, but it can sound a bit less sweary depending who’s listening.
Usage examples
"Who ordered five hundred napkins instead of fifty? Yeah, that was my cock-up. Now the office looks like a wedding venue in Wetherspoons."
"I made a right cock-up of the booking and reserved the table for the wrong Saturday."
"The whole rollout was a cock-up, half the emails went out blank and the rest twice."
"I’ve made a complete cock-up of the spreadsheet and somehow deleted the bit the boss actually needed."
"Don’t give me that look, I know it was a cock-up, but nobody died and the pub’s still open."
Where it comes from
It’s old British slang, in use by the late 1800s for a botched job or muddle. The exact force sits in that blunt, everyday British habit of naming a mess with a bit of bodily or rude flavour. It’s stayed alive as a very UK way to admit you’ve made a proper hash of things.