To read between the lines is to discern a meaning that isn’t made obvious or explicit.
This expression derives from a simple form of cryptography, in which a hidden meaning was conveyed by secreting it between lines of text. It originated in the mid 19th century and soon became used to refer to the deciphering of any coded or unclear form of communication… The first example that I can find of the phrase in print is from The New York Times, August 1862. Phrase Finder
I was reminded of this phrase by a pundit on cable news, so it’s funny that the 1862 citation is also from politics.
The letter assumes a somewhat enigmatical character, and the only resource we have is, as best we may, to ‘read between the lines’ of this puzzling, but important, communication of the British Foreign Secretary.