Barrington was born into a Christian family on the 8 July 1910. His father was Simon Joseph Cohen, a metal merchant and his mother was Elizabeth Harris and he had an older brother Jacques. Barrington converted to Judaism before marrying Betty Mayer Lotery in April 1935 and the family surname was changed legally from Cohen to Castle in May 1936 just before their son David was born. In 1939 they were living at St Georges Road in Westminster where Barrington was working as a metal merchant. He enlisted in 1940.

Barrington was training in Medicine Hat, Alberta, Canada when he was killed. His death certificate states: ‘1385530 L.A.C. Castle B.V. had completed one hour’s navigational training with his Instructor, F/O Rhodes. He was then sent solo in Oxford AR937 to practice navigational exercises. On his first take off at 15.50 hours he was seen to go into an almost vertical climb as soon as he left the ground, and then did a stall turn to the left into the ground. The aircraft was completely wrecked, and LAC Castle was seriously injured suffering a fractured skull and broken legs and arms, of which he died after admission to the Station Hospital. Subsequent inspection of the aircraft revealed that the tail trimming was within half a turn of being wound right back. The aircraft was the same in which Castle had received dual instruction from his Instructor immediately before. Wind – approx 25 m.p.h. No civilian personnel were injured on the ground’.