Green’s Dictionary of Slang

labdick n.

[abbr. Lothian and Borders Constabulary + presumably a link to dick n.5 (1)]

(Scot.) a police officer.

[Scot]I. Welsh Trainspotting 7: Raymie could detect a labdick in a crowded street the wey that sharks can sense a few drops of blood in an ocean.
[Scot](con. 1980s) I. Welsh Skagboys 395: Labdicks dinnae huv a fuckin scooby.