According to Eric Partridge's Dictionary of Catch Phrases, it is perhaps originally from the Royal Navy, though certainly used in that Service by 1920. There is nothing as specific as Fareham Creek mentioned. It was taken up by the Army and the RAF before becoming widely spread.
The fact that it was sometimes concluded as 'up salt creek' rather than the variant you mention might suggest that no such specific creek was intended. This was supposedly a reference to Salt River in the USA. Barking Creek in London also figured at one time.