Green’s Dictionary of Slang

mab n.²

a cab.

1821		W.T. Moncrieff Tom and Jerry I vii: A mab is a jingling jarvy! – a cabriolet, Jerry.
1845		G.W.M. Reynolds Mysteries of London vol. 2 142: Mabber Cab-driver.
1859, 1860		Hotten Dict. of Modern Sl. etc.
1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict.