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)]

[1960s+] a police officer, usu. male.

In compounds

noddy bike (n.)

[1980s] a police motorcycle.