Stroudley studied first at Clapham School of Art (1923-27), then later at the Royal College of Art (1927-30). His teachers included Thomas Monnington, A K Lawrence, William Rothenstien and Allan Gwynne-Jones. In 1930 he won a Major Abbey Scholarship which enabled him to travel mainly around Italy but also France, Germany and Holland for three years. Stroudley’s work indicates that these travels were highly influential in the development of his style. 

On his return from abroad Stroudley taught painting and print-making, showed his work and was given solo shows at Arthur Tooth and Sons and the Apollinaire Gallery. However, he had a mistrust of dealers and his career never quite reached the heights that his abilities seemed to justify. He had a caravan atop the cliffs of Rottingdean, where he would escape to paint, revelling in the massive forms of the cliffs, their textures and colours in all weathers.