Green’s Dictionary of Slang

have a cook v.

[rhy. sl., but note ety. of cook n.2 ]

to have a look.

[Aus]L. Esson Woman Tamer in Ballades of Old Bohemia (1980) 65: We were blowing down to Sorrento t’other day on one of them Bay boats. I was with the Heart and Arrow Push. Soon’s we had a cook at the engines, gorblime, we were pinched, five of us – two of them smart Ds picked us for being suspicious looking characters.
[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]Partridge DSUE (8th edn) 536: [...] C.20.