Green’s Dictionary of Slang

cakey adj.

also cake
[cake n.1 (1)]

stupid, foolish, ‘soft’.

J. Lawrence in Gilmour The Ruling Caste (2005) 21: He forbade his officers from going up in the hills for the hot weather and made known his disapproval of ‘a cakey man’ by which he meant someone [...] pretended to much elegance and refinement.
[UK]S.O. Addy Sheffield Gloss. 35: Caky, silly.
[UK]Barrère & Leland Dict. of Sl., Jargon and Cant.
[UK]G.F. Northall Warwickshire Word-Book 41: Cakey. Weak of intellect; silly.
[US]M.G. Hayden ‘Terms Of Disparagement’ in DN IV:iii 213: cakey, foolish; below par. ‘This composition sounds cakey’.
[UK]M. Marshall Tramp-Royal on the Toby 98: It wasn’t long before I was completely cakey, doolally.
[UK]R. Grinstead They Dug a Hole 54: Why should they tell us a cakey bar like that if we’re in the Med?
[UK]K. Sampson Outlaws (ms.) 90: Paul told us it stands for Young Men’s Cock. Which is a bit cake, to be fair.