The Scot half of my family have a cupboard by their chimy called a press, though its just a normal cupboard. No one seems to know why it's called this, although there had been some preculation.....any one know (QM?)
The earliest-recorded use of 'press' to mean 'cupboard' is actually in Chaucer's 'Miller's Tale' published in the 14th century, so it's an old usage. It is nowadays, as you suggest, more commonly used in Scotland. I'd imagine it got the name from the concept of things being stacked up on its shelves, as 'press' can also mean 'crowd' in the sense of lots of people crammed together.
Yep, hot press is the common name for airing cupboard in Ireland.Oddly enough though, I'm living in Scotland and none of the Scots I work with knew what I mean when I called a cupboard a press - apparently up in the North East it's a term only used by "auld wifies", rarely heard except in the wilds! (Their words not mine I hasten to add....)