Green’s Dictionary of Slang

nod n.2

also noddy, noddy man
[? from the policeman (‘Mr Plod’) in the Noddy books (cf. plod n.2 ), created by author Enid Blyton (1897–1968)]

a police officer, usu. male.

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[UK]Gandalf’s Garden 6 n.d. 11: nods or noddy men ordinary policemen on the beat: (From Mr Plod, the policeman, in Noddybooks).
[UK]T. Blacker Fixx 97: The police [...] shipped in spare noddies from the provinces.

In compounds

noddy bike (n.)

a police motorcycle.

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[UK]J. Morton Lowspeak 105: Noddy bike – a police motor cycle.