Green’s Dictionary of Slang

Barking creek n.

SE in slang uses

In phrases

have been to Barking creek (v.) (also have been to Barkshire) [pun]

to have a very bad cough (cf. member for Barkshire under member n.² ).

1823

‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 6: Barking creek persons troubled with a short cough are said to have been there, or to Barkshire.