Connolly was born at Bath, the son of Vice-Admiral Matthew Connolly, R.N., and his wife Harriet Kemble. He was educated at Haileybury College and trained at the Royal Military College, Sandhurst. He was commissioned into the King's Own Yorkshire Light Infantry as a second lieutenant on 7 November 1891. He was promoted captain on 26 July 1899. He was appointed adjutant of the 2nd Volunteer Battalion, Royal Warwickshire Regiment on 23 April 1900, and held that position until 23 April 1905, and returned to regimental duties on 6 May. From this point much of his service was in South Africa, He was promoted major on 9 July 1910. While in South Africa, Connolly took an interest in minerals and then started observing snails in the field. He took up malacology and conchology seriously and became an authority on the land and freshwater molluscs of South Africa. On 11 December 1912, he went onto the half-pay list as a result of ill-health arising from rheumatic fever. He retired from the army on 2 May 1914. During World War I he was employed at the army record office. He became a friend of Edgar Albert Smith, who was keeper of molluscs at the British Museum and who recognised his worth. In 1918, Connolly became an honorary scientific worker in the natural history department at South Kensington and continued to work there until December 1946 in spite of increasing lameness. Connolly published some fifty papers on molluscs between 1910 and 1945. He was a member of the Malacological Society from 1908 to 1938 and was president of the Conchological Society in 1930. Connolly was also a connoisseur of wine and an expert on potted meats and wrote a highly regarded pamphlet on the subject. Connolly married Muriel Maud Vernon, daughter of Colonel Edward Vernon, J.P., D.L., of Clontarf Castle, Co. Dublin, whom he met while serving in Ireland. They lived at The Lock House, Deepcut, Surrey on the Basingstoke Canal, although Connolly was based mostly in South Kensington. Their only child was the writer and critic Cyril Connolly. Tom Pain, a younger researcher and friend of Connolly, recalled being introduced to Cyril Connolly by his father with the words "this is my son — he is a fool!"
