Green’s Dictionary of Slang

on the cot adj.

In phrases

on the cot (adj.)

(UK milit.) teetotal.

[UK]‘Army Slang’ in Regiment 11 Apr. 31/2: A teetotal [soldier] is ‘on the cot,’ ‘on the steady,’ ‘on the tack,’ ‘on the dead,’ or has ‘put the peg in’.