Born on April 24, 1940, Northcott read English at Oxford University and received a Bachelor of Arts degree from Oxford in 1962. He then taught English from 1964 to 1970 and developed an interest in composition. He went on to study at the University of Southampton, where his instructors included Goehr and Jonathan Harvey.

Following his studies, he became a music critic for the New Statesman, for the Sunday Telegraph and was chief music critic of The Independent. He also wrote on music for Tempo and BBC Music Magazine.

Outside his work as a critic, he also composed various works such as an Oboe Sonata (1978), Guitar Fantasia (1982), and a Piano Sextet (1985, premiered by the Fires of London). He also composed several Choral pieces and Concertos. His works went on to be performed at the Proms in 2016. He also wrote two books, “The Music of Alexander Goehr: Interviews and Articles” and “The Way We Listen Now and Other Writings on Music.”