Born in London in 1911, Nockolds was a largely self-taught artist. His early aptitude for depicting shapes and movement was discovered very early in life when, as a child, the artist made observational drawings based on the bi-planes he saw flying over England during the First World War. His interest in aviation soon developed, and by the mid-1920s Nockolds began to forge a name for himself as an eminent motoring and automobile artist. He frequently contributed illustrations to publications such as Autocar, Motor and Motor Sport magazines and quickly came to be considered among the pioneers of motoring art. Nockolds was particularly skilled in conveying movement and light, aspects which brought an inimitable depth to his compositions.

During the Second World War, Nockolds served as an Official War Artist in the Royal Air Force. The artist received several commissions, notably by the Fighter Command and the Ministry of Information, to portray important moments of the Battle of Britain in his distinctive painting style. His work depicting great aviation battles and fighter planes are considered to be among the most enduring representations of the War. Nockolds continued to paint automobiles following the War, and his reputation as an acclaimed artist grew from strength to strength. Though best known for his depictions of motoring and aviation subjects, Nockolds was also an accomplished landscape and portrait painter who often produced marine and animal studies. He exhibited at the Royal Academy in 1949, and regularly exhibited at the Royal Society of Marine Artists and the Royal Society of Portrait Painters. Nockolds was elected Chairman of the Guild of Aviation Artists in 1975, and continued to paint late in to his life. His work is represented in a number of collections, including that of the Imperial War Museum.