Green’s Dictionary of Slang

a woman, usu. a prostitute or at least an ‘enthusiastic amateur’, who dominates her surroundings.

1892		Proc. Old Bailey 14 Nov. 97: The children followed through the woman being three-parts drunk, and they were calling out ‘Tottie Fay!’—I think the woman answered it.
1984		Partridge DSUE (8th edn) 1255: [...] C.20. The fie is of exclamatory origin (‘Oh my!’). [...] Hence, Totty Fay (Pronounced Fye), alternatively Tottie Hardbake, a female assuming a haughty air: derisive Cockney: since ca. 1890.