Extract from OED Online

mickey, n.¹

DRAFT REVISION Dec. 2001

[< Mickey, pet-form of the male forename Michael (see MICHAEL n.). Cf. MICK n.¹, MIKE n.⁴, -Y⁶.
In phrase to take the mickey at sense 7 perh. after Mickey Bliss, rhyming slang for piss. Cf. earlier MIKE n.⁷]

7. colloq. (chiefly Brit.). to take the mickey (out of): to behave or speak satirically or mockingly; to make fun of, satirize, or debunk (a person or thing). Cf. MIKE n.⁷, PISS n. 2.

1948 A. BARON From City, from Plough vi. 49 ‘Higgsy,’ said the sergeant, ‘they think I'm taking the mickey. Tell 'em.’ 1952 ‘J. HENRY’ Who lie in Gaol iv. 66 She's a terror. I expect she'll try and take the mickey out of you all right. Don't you stand for nothin'. 1957 L. P. HARTLEY Hireling 134 He had no great regard for Constance, except in so far as she sometimes took the mickey out of Hughie. 1958 Observer 28 Dec. 3/1 ‘Tonight’ is not only a tough and irreverent programme, but glib and smart and anxious to take the mickey. 1960 E. W. HILDICK Jim Starling & Colonel ix. 76 The servers must have thought that no boy would dare to take the mickey in such circumstances. 1971 B. W. ALDISS Soldier Erect 101 Geordie looked anxiously at me, in case I thought he was taking the micky too hard. 1991 Sunday Sun (Brisbane) 3 Feb. 6/5, I don't think there is any subject that is too serious to take the micky out of.