Jack began a medical training at Cambridge University, achieving his First M.B. (roughly equivalent to science A-levels) before announcing to his initially disappointed father that he wanted to become an artist.

He attended St Martin's School of Art in London from 1929 to 1932 (aged 18 to 20) and, apparently at his parents' request, his cousin Barbara Hepworth and her first husband the sculptor John Skeaping, already established artists, took Jack under their wing. "It was not long before they split up and when Ben Nicholson took Barbara over he took me over as well."  Jack was Ben Nicholson's pupil from 1932 to 1936.

During the 1930s Jack lived at 22 Parkhill Road, Belsize Park NW3 close to The Mall Studios. At different times he also lived at 41 Parkhill Road and 87 Haverstock Hill. In the pre-war years The Mall Studios were occupied by Cecil Stephenson, Herbert Read and Jack's cousin Barbara Hepworth, initially with John Skeaping and later with Ben Nicholson. Close neighbours in Parkhill Road included Henry Moore, Naum Gabo and Piet Mondrian. Jack worked as an abstract painter, using the name Arthur Jackson, and as a photographer of works of art and art exhibitions.  His paintings were shown in a number of London and provincial exhibitions.
I think 'abstract' is as good as anything. The great majority of my paintings are non-representational.

By the time I was just starting to exhibit, in the same shows as Barbara, about 1934, Barbara was already well established.  It seemed to our mutual advantage, to avoid inevitable confusion and comparison, not to be showing under the same name. The simple solution was for me to adopt, for painting purposes, my baptismal names.  Jackson was my mother's maiden name. I do not think this is so extraordinary. Many people adopt a nom-de-plume although more often writers. Did not Le Corbusier do exactly the same thing to avoid confusion with his brother Jeanneret?  Clearly, in my case, the ruse was not entirely successful. It just made another talking point.
In working alongside Ben and Barbara, who were both significantly older than him and were now at the forefront of the modern movement, Jack accepted that he was a "mere student on sufferance" who never actually met Ben's family or their close friends: "However, I did know Henry Moore (who did not altogether approve of me) and sometimes worked for him roughing out, as I did for Barbara."

He became acquainted with many significant figures of the modern movement in addition to those already named, including Naum Gabo, Piet Mondrian, Winifred Nicholson and, most significantly for his future career, the architects Leslie Martin and his wife Sadie Speight.

Winifred Nicholson was Ben's first wife and an established painter in her own right.  She invited Jack to stay in her house in Cumberland in the summer of 1936 where he made two large abstract paintings and did some photography. She gave him a Cumberland sheepdog. As time went on he encountered other well-known artists including John Piper and Piper's first wife the constructions maker Eileen Holding, as well as Ceri Richards, Ivon Hitchens and the sculptor Elizabeth Spurr.  His knowledge of contemporary art widened as he made several trips to France and Switzerland, meeting Jean Hélion and Hans Erni and paying a visit to Mondrian's studio in Paris.  Mondrian subsequently moved to London in 1938, taking a studio in Parkhill Road, before leaving for America in 1940. 

The outbreak of war in 1939 meant that Jack stopped painting sometime in 1940 and it eventually also interrupted his architectural activity.  He did not paint again - beyond refurbishing paintings for retrospective exhibitions - until after he retired in 1976.  He then began to produce new work, carrying on stylistically from where he had left off thirty five years earlier.
From a letter to David Buckman, December 1993: