What’s the origin of the phrase ‘Down the pan’?
The pan is the lavatory pan. This phrase is of UK origin and is fairly recent. The first record of it in print is in the 1961 edition of Eric Partridge’s A Dictionary of Slang and Unconventional English:
“Down the pan… A Cockney equivalent of down the drain, ruined with no chances left.”
The US has an equivalent expression - ‘down the tubes’.