In 1934 he claimed what was to remain his career-best innings return of 6–44 against HDG Leveson-Gower's XI at Reigate.
Singleton later recalled that in Worcestershire's match against the Australians in 1938 he just failed to hold on to a catch at leg slip that would have dismissed Bradman for nought: in the event he went on to score 258!
In Worcestershire's final game before the outbreak of war, Singleton made the first of his four centuries, hitting an unbeaten 102 against Nottinghamshire, and when county cricket resumed in 1946, Singleton was made captain of Worcestershire, and enjoyed the most productive summer of his career: he scored 1,773 runs in first-class cricket at an average of 34.09, as well as taking 43 wickets at 28.23.
Whilst serving with the Royal Air Force in Rhodesia during the war, Singleton had met his wife Polly; they married in 1941 and had five children: three sons and two daughters.
After the end of the 1946 English season they emigrated to Rhodesia permanently, and although he concentrated on farming, he played nine times for the Rhodesian side between 1946–47 and 1949–50, once again being appointed as captain.