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]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?