He was the son of George Wolfenden an education official and Emily Hannah Gaukroger both born in Halifax, Yorkshire. George Wolfenden became an official of the West Riding Education Authority based in Wakefield, Yorkshire, where John Frederick Wolfenden attended Queen Elizabeth Grammar School. He won a scholarship to Oxford and became a don at Magdalen College, Oxford, in 1929. John Wolfenden was the headmaster of Uppingham (1934–1944) and Shrewsbury (1944) and chairman of various government committees which mostly focused on education and problems with youth.
Wolfenden chaired an independent committee initiated by the Central Council of Physical Recreation in 1957, which investigated the role of various statutory and voluntary groups in sport in the UK. The committee published its report in 1960 and it remains an influential work in its field.
In 1969, he was appointed as director of the British Museum, a post that he left in 1973. In 1974, he was made a life peer as Baron Wolfenden, of Westcott in Surrey.