 Kennedy's grandfather was Lauri Kennedy, principal cellist with the BBC Symphony Orchestra, and his grandmother was Dorothy Kennedy, a pianist.Lauri and Dorothy Kennedy were Australian, while their son, the cellist John Kennedy, was born in England.After graduating from the Royal Academy of Music in London, at age 22, John joined the Liverpool Philharmonic Orchestra, later becoming the principal cellist of Sir Thomas Beecham's Royal Philharmonic Orchestra.