 Ashby was knighted in 1956, and was created a life peer as Baron Ashby, "of Brandon in the County of Suffolk" on 6 July 1973.Ashby was secretary of the Society for Experimental Biology from 1935 to 1938 and president of the British Association for the Advancement of Science from 1962 to 1963.He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1961.