Ashmore was born on the 21 February 1893, the eldest son of Arthur Haliburton Ashmore. In 1919 he married Tamara Vasilevna Shutt (who died 1972) with whom he had 2 sons.
He was educated at Sandroyd, then at the Royal Naval Colleges at Osborne and Dartmouth.
Ashmore's naval career included service in submarines during World War I (1914-1918). In 1915 he was made a Lieutenant; commanded HM Submarines C35, V3, E46, and subsequently L52; became a Commander in 1928 at the Royal Naval Staff College; then commanded HM ships Wallflower and Cyclamen; became a Captain in 1934 at the Imperial Defence College; then commanded HM ships Kent, Valiant and Malaya; became Rear-Admiral in 1944; and was Flag Officer commanding the Reserve Fleet (1945-1947). In 1947 he joined the retired list and became Vice-Admiral (retired, 1948).
Ashmore died on 10 January 1974.
The collection comprises material relating to Ashmore's active service in World War I in the Baltic and Russia; material for a naval lecture (1938) and correspondence with Admiral of the Fleet Sir Edward Ashmore relating to Ashmore's career.
The collection was deposited at Churchill Archives Centre in 1989.
The collection is owned by Churchill College.