Green’s Dictionary of Slang

cold potato n.2

[rhy. sl.; note Cockney pron. ‘pertater’]

a waiter (cf. hot potato n.2 ).

[UK]J. Franklyn Dict. of Rhy. Sl. 52/2: Cold Potato Waiter. Current in theatrical world.
[UK]S.T. Kendall Up the Frog.
[UK]R. Puxley Cockney Rabbit.
[UK]B. Kirkpatrick Wicked Cockney Rhy. Sl.