Green’s Dictionary of Slang

nanny n.²

(UK Und.) the head.

1791

Confessions of Thomas Mount 18: Head, nanny.

In phrases

lose one’s nanny (v.)

to lose one’s head.

1908

K. McGaffey Sorrows of a Show Girl Ch. viii: When he saw me sitting there having the time of my young life he lost his nanny and caused a scene.

off one’s nanny (adj.)

mad.

1894

‘Banjo’ Paterson ‘Hughey’s Dog’ in World of Banjo Paterson (1967) 29: ‘Off his nanny again,’ thought the boss, ‘the sooner he goes the better.’.