Henry Carey composer of "God save the King"
In Jahrbücher für musikalische Wissenschaft ; 1.1863 the editor Friedrich Chrysander gives a lengthy article about the life and works of H. Carey. Here he cites a letter from a doctor to the son of the late H. Carey where he states that Carey had given the tune in question to one of his patients, J. C. Smith, asking to correct the general bass.
The song was written in 1743 originally not as a national anthem, but with only two verses as a parting song for king George when leaving for Germany to lead his troops in the war vs. the French. So the omitted second verse makes sense. By the way, the war ended with the splendid victory at Dettingen, and so English music owes this war two famous pieces: The National Anthem and the Dettingen Tedeum, by Händel.

Wilfried