Along with composer Derek Bourgeois he played tuba in the National Youth Orchestra of Great Britain.
He returned to the tuba upon his graduation from studying Natural Sciences at Pembroke College, Cambridge.
In autumn 1964, he moved to London, where he was appointed Principal Tuba of the BBC Symphony Orchestra.
He taught many UK professional tubists, including Patrick Harrild, who succeeded Fletcher as the LSO's principal tuba.
The John Fletcher Trust Fund was established after his death, in his memory, to provide bursaries for young brass players to attend the courses run by the National Youth Orchestra, National Youth Brass band and other training centres.