Taking the mickey

Generally believed to be a softened version of the cruder "taking the piss," itself thought to come from Cockney rhyming slang, where "Mickey Bliss" rhymes with "piss." Rhyming slang regularly got shortened to just its first word, turning "Mickey Bliss" into simply "Mickey" or "the mickey," giving speakers a way to say the same thing without the crude original. It's a well-supported theory given how rhyming slang typically behaves, though, as with a lot of slang, nobody wrote down the exact moment it was coined.