He was in active service in the Second World War. He later commanded two frigates before achieving high command in the Navy. He served as First Sea Lord and Chief of the Naval Staff in the mid-1970s. He went on to be Chief of the Defence Staff, serving briefly. In retirement he became a Director of Racal Electronics and a Governor of Suttons Hospital in London.
Ashmore died on 28 April 2016 in London at the age of 96.