Green’s Dictionary of Slang

nanny (goat) n.

[rhy. sl. ]

1. the Totalizator [Tote n.].

[UK]S.T. Kendall Up the Frog.
[UK]J. Jones Rhy. Cockney Sl.
[UK]Partridge DSUE (8th edn) 777: since ca. 1925.
[UK]Guardian Sport 98 31 Jul. 15: The unsettled Dwight Yorke [...] is still available at 14-1 with the Tote. The Nanny has has taken the view that [...] he too will have to share the goals.
[UK]B. Kirkpatrick Wicked Cockney Rhy. Sl.
[Aus]T. Peacock More You Bet 74: The ‘tote’, which is short for the ‘totalisator’, which is colloquially known as ‘the machine’, [...] the ‘giddy goat’, or the ‘nanny goat’.

2. a boat.

[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]J. Jones Rhy. Cockney Sl.
[UK]Partridge DSUE (8th edn) 397: since ca. 1930.
[UK]M. Coles Bible in Cockney 16: Noah and ’is Big Nanny Goat. [Ibid.] 83: They got into a nanny and headed off to a quiet place.

3. a coat.

[UK]J. Jones Rhy. Cockney Sl.
[UK] (ref. to 1940s) R. Barnes Coronation Cups and Jam Jars 164: Gi’us me nanny goat off that nail, will you, son?
[UK]P. Wright Cockney Dialect and Sl. 108: ‘Nanny-goat’, coat.
[UK]Partridge DSUE (8th edn) 777: later C.20.
[UK]B. Kirkpatrick Wicked Cockney Rhy. Sl.

4. the throat.

[Aus] ‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxvi 4/2: nanny goat: Throat.
[Aus]R. Aven-Bray Ridgey-Didge Oz Jack Lang 37: Nanny Goat Throat.
[UK]B. Kirkpatrick Wicked Cockney Rhy. Sl.