Born in Hastings, Sussex, John was the third son of a clergyman, and his early years were spent in West Dean, near Goodwood. He studied law at St John's College, Oxford and then St John's Wood School of Art in London before and after the 1914-18 war, enlisting in the Royal Field Artillery during the conflict. During WWII he was an Official War Artist. 

In 1945, Armstrong moved to Oriental Cottage, Lamorna in Cornwall, which was a cottage belonging to his second wife, Veronica Sibthorpe.  He remained engaged in painting surrealist murals for the London stage which he had been successful with, both for stage and film. Special friends were Elsa Lanchester and Charles Laughton.

In Cornwall he joined with John TUNNARD, Peter LANYON and others irritated by the division of art into categories of figurative and non-figurative by the Penwith Society, and began to show his work at NAG, becoming a re-invigorating force within the NSA which they all joined. Armstrong served on the organising Committee of the Newlyn Society of Artists until 1955 when he resigned from both the Society and the Committee, due to leaving Cornwall.

In the early 1950s when Armstrong had been commissioned to paint the ceiling mural for the Bristol Council House, he did this work on canvas in the lower front room of NAG (where administration offices are today) which he contracted to rent for a year (1954).  The canvas was so large that it had to be wound around three giant rollers, from which it was unwound as needed and painted a section at a time. An assistant for the year was a young woman named Mary COLLETT, who has continued as a painter in her own right. Later the canvas was 'marouflayed' (stuck) to the Council House ceiling where it remains.

In 1955 he returned to London, divorcing from Sibthorpe, remarrying thereafter to this third wife, Annette.  Armstrong was made an Associate of the RA in 1966. He also painted murals for the Royal Marsden Hospital. Precise but muted in colour, his symbolist qualities are keynotes of his style, and always his work was abstract, upon occasion surrealist.

In 1989, a painting by John Armstrong, from the Permanent Collection of NAG, Veronica as Harlequin, was chosen for the Cornwall County Council Exhibition, 'A Century of Art in Cornwall 1889-1989' in which 140 paintings executed in Cornwall over the 100 year period were shown. The painting had been given to NAG by Frankie FREETH, another artist who had served with Armstrong on the NAG committee, and a close friend and partner to his ex-wife Veronica.