I was just watching a British crime show and learned that the prisons are part of Her Majesty’s Prison System (or some such).

I daydreams of becoming an indie game developer and publishing under the name Her Majesty's Pencil Service

That name was inspired by the very real HMSO: Her Majesty's Stationary Office(!): a name that struck me as absurdly pretentious for something really mundane.

Hence the phrase "detained at Her Majesty's pleasure".