Parsons was born in Bristol as the eldest son of Ernest Parsons, a paint manufacturer (Black Friar Paints), and Ellen Mary Hill.
His younger brother Dick Parsons was a championship rifle marksman with the British Army, and his cousin Patrick Seager Hill was a clothing manufacturer, and a pioneer and developer of fire protective clothing.
He was educated at Clifton College, then later at Cambridge University, where he studied estate management, and became a farmer in the Salisbury, Wiltshire area.
In the 1950s he became the liaison officer for the South Western Division of the Ministry of Agriculture, and for this he was made a Commander of the Order of the British Empire (CBE) in the 1963 Birthday Honours.
He was then appointed a Commissioner of the Crown Estates by Queen Elizabeth II, for which he was made a Commander of the Royal Victorian Order (CVO) in the 1973 Birthday Honours.