At the age of 14, Harrison was apprenticed to a pharmacist, at the end of which he was awarded the Royal Pharmaceutical Society's Jacob Bell Scholarship. As a student, he was awarded medals in chemistry, botany and materia medica. He qualified as a pharmaceutical chemist in 1891, becoming a demonstrator in the Society's laboratory and school. He later became head of the analytical laboratory at Burroughs & Wellcome, and assisted in the compilation of the British Pharmaceutical Codex.
At the outbreak of World War I, Harrison tried to enlist in the British army, but was rejected on account of his age (45 at the time), but was accepted as a corporal into a "sportsman's battalion" in 1915. However, after the first use of gas weapons by the German Army in 1915, the British War Office enlisted chemists, including Harrison, to find a way of defending against such weapons.
Harrison produced the large box respirator, the first serviceable British gas mask., and continued to work tireless for the remainder of the war. His continued improvements saw him repeatedly promoted, reaching the rank of Lt Col in the Royal Engineers. Harrison died of pneumonia at 47, one week before Armistice Day.
In a letter to his widow, the Minister of Munitions, Winston Churchill, wrote "It is in large measure to him that our troops have been given effectual protection from the German poisonous gases"., and that he would have been promoted to Brigadier-general in charge of all chemical warfare .
The Edward Harrison Memorial Prize of the Royal Society of Chemistry is named in his honour.