Green’s Dictionary of Slang

cob n.5

In phrases

have a cob on (v.) [? dial. cob, to strike or cob a lump, a large piece, thus cf. SE colloq. phr. have a chip on one’s shoulder]

to be in a bad temper, to be annoyed; thus cobby adj., angry.

[UK]Partridge DSUE 163/2: Have a cob on, to be annoyed: ships' stewards'.
[UK]F. Laskier Log Book : The boy [...] grinned at his boss and whispered, ‘What’s bit the old man? ’e seems to have a proper cob on this morning’.
Lancs. Dialect Soc. Jrnl 1-8 40: The citizens suffer fools (GOMS) g'adlyy enough even when they HAVE A COB ON (carrying a load of annoyance, in a temper) .
[UK]M. Evans Diary 30 Jan. cited in Guardian 6/12/2021 🌐 I switched off the power, starting with George’s amplifier, just as they [i.e. the Beatles] were about to break into a new number. Then George got a right cob on.
[UK]A. Bleasdale ‘Jobs for the Boys’ in Boys from the Blackstuff (1985) [TV script] 39: I don’t know why Dixie’s got a cob on with us for.
[UK]N. Griffiths Stump 73: — Still got a cob on, Da? [...] Da. you still cobby, mate?