After studying at the Collège de Lausanne he won a scholarship to Oriel College, Oxford, reading French and German.
He also took part in Operation Archery, a commando raid on port Vågsøy, Norway and helped support Greek resistance fighters in liberating Kalamata.
After the war, Coate joined the UK Foreign Office with diplomatic postings to Salonika, Oslo, Leopoldville, Rome, The Hague, Buenos Aires, Stockholm and finally Brussels at which point he took early retirement in 1967.
Coate's first maze commission, The Imprint of Man, was completed in 1975 for a private garden at Lechlade Mill in Gloucestershire.
These included: In 1955, Coate married the painter, Pamela Dugdale Moore, with whom he raised two daughters, Caroline and Penelope.