pat and mike, n.¹ — Green’s Dictionary of Slang

pat and mike n.¹

also Irish mike

[rhy. sl. = SE bike]

a bicycle.

1912		Sport (Adelaide) 3 Aug. 14/3: They Say [...] That Jack N. wants to sell his ‘Pat and Mike ’ before he gets hitched up.
1930		(con. 1914–18) Brophy & Partridge Songs and Sl. of the British Soldier.
1960		J. Franklyn Dict. of Rhy. Sl.
1972		Dodson & Saczek Dict. of Cockney Rhy. Sl. 30: Irish mike. Bike.
1992		R. Puxley Cockney Rabbit.