Hate to be that guy, but: https://en.wiktionary.org/wiki/posh:
'Most likely derived from Romani posh (“half”), either because posh-kooroona (“half a crown”) (originally a substantial sum of money) was used metaphorically for anything pricey or upper-class, or because posh-houri (“half-penny”) became a general term for money. [...]
A popular folk etymology holds that the term is an acronym for "port out, starboard home", describing the cooler, north-facing cabins taken by the most aristocratic or rich passengers travelling from Britain to India and back. However, there is no evidence for this claim.'