[1][2] Pelham was born at 20 Bradmore Road in North Oxford,[3] the eldest son of classical scholar Henry Francis Pelham, President of Trinity College, Oxford, and Laura Priscilla Buxton, daughter of Sir Edward Buxton, 2nd Baronet.

John Thomas Pelham, third son of the 3rd Earl of Chichester, whose father, the 2nd Earl, was a first cousin of Prime Ministers Henry Pelham and Thomas Pelham-Holles, 1st Duke of Newcastle.

[1] At age 24, Pelham joined the Board of Education and steadily advanced.

Irene Lubbock, fifth and youngest daughter of John Lubbock, 1st Baron Avebury and Alice Augusta Laurentius Lane-Fox, daughter of Augustus Pitt Rivers.

They had two sons and three daughters:[2] He died in 1949 in Oxford as a result of an accident, two days before his 73rd birthday.