As an undergraduate, he held a scholarship, played soccer for Cambridge University and hockey for Cambridgeshire, was in his college's cricket First XI and crowned his first four years with a double first in the Natural Science tripos.
From 1940 to 1945, Ashmore served in the Royal Air Force, rising to the rank of Squadron Leader.
During his career, Ashmore published many scientific research papers, especially in Nature, the Journal of Catalysis, and Science.
An early report in Nature in 1951 of a 'lighthouse reaction' was later recognized as important, and a paper to the 5th International Combustion Symposium at Pittsburgh (1954) was much cited.
From 1965 to 1972 he was joint editor of the periodical Combustion and Flame In 1943, Ashmore married Ann Elizabeth (Betty) Scott, and they had three sons and one daughter.