an unfashionable individual; someone who is innocent, or foolish; a fool. Possibly originates in the name Wally, however Scottish dialect wally-draigle (a feeble, ill-grown person) may well have had an influence UK, 1969.

in CID slang, a uniformed police officer, especially a constable; more generally, a trainee or an incompetent police officer. 'Woolly' is also recorded by the Oxford English Dictionary in 1965 UK, 1970