Green’s Dictionary of Slang

coffee and cocoa v.

also cocoa
[? rhy. sl. though note Quinion (https://www.worldwidewords.org) ‘Though it has been recorded in the longer forms coffee and cocoa and tea and cocoa, these look like afterthoughts, attempts to force an existing saying into the standard mould (if these were genuinely the original forms, one would expect to hear coffee and teaas short forms, but one never does)]

say so; usu. as I should cocoa

[UK]J. Curtis Gilt Kid 22: What with the steamer she’s got for regular and the odd ones she picks up she don’t do so bad, I should cocoa.
[UK]J. Curtis They Drive by Night 79: ‘Takes a bit of bleeding doing.’ ‘I should cocoa.’.
[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]Dodson & Saczek Dict. of Cockney Rhy. Sl.
[UK]R. Puxley Cockney Rabbit.

In phrases

I should cocoa (also I should coco, I should cockle)

you must be joking, don’t make me laugh [esp. popular in BBC Radio’s Billy Cotton Band Show in the 1950s].

[UK]N. Mitford Pigeon Pie 25: I’m not so very strong. I should cockle.
[UK](con. 1939) R. Westerby Mad in Pursuit 170: Who – me? For Jackson? I should cocoa!
[UK]P. Hoskins No Hiding Place! 190/2: I should cocoa. I should say so, or I should imagine.
[UK]D. Powis Signs of Crime 178: Cocoa, I should ‘I should think so!’.
[UK]Rhoda with Specials A.K.A. ‘The Boiler’ 🎵 I bought you all them drinks and then you want to go home. I should blinkin’ cocoa.
[UK]Indep. Rev. 24 Aug. 2: I should cocoa! Chance would be a fine, fine thing!
[UK]Indep. on Sun. Real Life 21 Nov. 3: I think my answer was that ‘I should coco’.
[UK]Guardian Sport 1 Apr. 12: Misled? I should co-co.
[UK](con. 1945) M. McGrath Silvertown 163: Well, would you cocoa? laughs Len Page.
[UK]Guardian Guide 13-19 Jan. 21/1: [headline] I should Coco.
[UK]J. Meades Empty Wigs (t/s) 170: Horrocks asserts that Jervoise and Mein Opa could both ride to their places of learning in little more than hour and a half. I should cocoa!