OED for posh gives 1918 slang perhaps derived from 19th century posh meaning money or a dandy (origin unknown). On this historical use of posh, my dictionary of historical slang says: "1.money; specifically a halfpenny or other coin of low value (~1839) from Romany posh = a half, as in posh-horri a halfpenny and posh-koorona a half-crown 2. a dandy ...(~1897) possibly derived from 1. or a corruption of (big) pot"