Reay Parkinson was born in Edinburgh on 15 February 1893, the son of Thomas Wright Parkinson and Euphemia Jessie Parkinson (née Pitman). He joined the Royal Navy as a Cadet on 15 January 1906. He was promoted to Midshipman on 15 September 1910 and on 5 December 1911 he was appointed to the cruiser HMS HAMPSHIRE. He was promoted to Sub Lieutenant on 15 January 1914 and on 25 June 1914, Reay Parkinson was appointed to the cruiser HMS MINOTAUR.

On 10 February 1916, Reay Parkinson was appointed to the Submarine Depot Ship HMS FORTH ‘for Submarine Duties‘. This was followed by an appointment to HMS W2 as First Lieutenant on 1 April 1916. Reay Parkinson was next appointed to HMS E49 as First Lieutenant on 1 November 1916. On 12 March 1917 E49 was lost with all hands when the submarine hit a mine off Huney Island in the Shetlands.

Reay Parkinson had married Miss Bluebell Hooper on 14 June 1916.  He is commemorated on the Portsmouth Naval Memorial on Panel No. 24.