He was born into a Scottish family, the son of James Alexander Leo Henderson and Maud Sophia Grace Hardy. Henderson was educated at Dragon School and Stowe School and Magdalen College, Oxford. He served with the Scots Guards during the Second World until he was seriously wounded in 1944 during the Battle of Anzio, sustaining series injuries from which he never fully recovered, despite undergoing multiple operations over the years. His brother John Patrick Leo Henderson was killed in action in Italy in 1944.