In the United Kingdom, The Privileged Presses are Cambridge University Press and Oxford University Press. They are called this because only they, along with the monarch's private printer, have the right to print the Book of Common Prayer and, within the UK itself, the Authorized Version of the Bible. These two books are under perpetual copyright to the crown.
The King's Printer is chosen by each monarch by patent letter, but the two university presses derive their printing rights from their charters. The Cambridge University Press charter from 1534 gives it the right to print "all manner of books," which means that the royal copyright is not excepted. The Oxford University Press received a similar right when it was chartered in 1634.