I am sorry to disappoint anyone who believes the urban myth that a certain turpiloquy originated as an acronym of this phrase - it is absolute nonsense. The English word "f**k* ultimately shares a common indo-european ancestry with the Italian word "ficcare".
Grammatically, "under consent of the King" is not correct. It should be "by consent of the King". And I repeat - it was never the case that the common people of England required the consent of the King to enjoy natural relations. This is complete fiction.