Morse was born in Kensington, London, in 1928, the only son (he had a younger sister) of Francis John Morse, of Lenwade House, Norwich, and his wife, Kinbarra, daughter of barrister Edward Armfield-Marrow.[3][4] Francis John Morse, the second son of Sir George Henry Morse, a brewer and Lord Mayor of Norwich from 1922 to 1923, was from a junior branch of the landed gentry Morse family of Lound, Suffolk.[5] The family were Quakers.[4]
A career banker, Morse began with Williams and Glyn's Bank and went on to be chairman of Lloyds Bank between 1977 and 1993; assuming the role at age 48, he was the youngest head of a clearing bank.[4] He served on the Board of the Bank of England as an executive director from 1965 to 1972, and as a non-executive from 1993 to 1997.[8] He was also the first Chairman of the International Monetary Fund's Committee of Twenty (C20).[9] In the 1975 New Year Honours, he was appointed Knight Commander of the Order of St Michael and St George (KCMG) "for services to the reform of the international monetary system".[10]
He had a keen interest in cryptic crosswords and was a skilful writer of clues.[4] His record of success in the clue-writing competitions of Ximenes and Azed was such that Azed's December 2008 Competition puzzle was dedicated to the occasion of his eightieth birthday.[11] He had puzzles published under the pseudonym "Esrom" (his surname in reverse).[12]
In 1955, Morse married Belinda Marianne Mills, the daughter of Lt-Colonel Robert Breynton Yarnton Mills, OBE, MC, of the landed gentry Mills family of Sudgrove;[16] they had three sons and two daughters (one of whom died from leukaemia at the age of four).[4]