During the Second World War Drayson was decorated for sinking the German Navy auxiliary cruiser Komet. After the War he returned to Cambridge, graduated, and taught at St. Lawrence College and Felsted, then was head master of Reed's School and Stowe before becoming lay chaplain to the Bishop of Norwich.
Born in Ramsgate, Kent, Drayson was educated at Chatham House School, St. Lawrence College, Ramsgate, and Downing College, Cambridge, arriving there in 1938 to read Modern Languages. At school he excelled at field hockey, cricket and middle-distance running.
The Second World War broke out when Drayson had been at Cambridge for a year. He joined the Royal Navy as a rating, but was sent to take an officer training course at the newly established HMS King Alfred, then at Hove. After joining the fleet he spent the whole war serving in the motor torpedo boats of the home coastal forces. Shipping on board MTB 236 as her first lieutenant, he was given temporary command of her in 1942, with the rank of Acting Sub-Lieutenant, shortly before the MTB took part in an action off Barfleur which sank the German auxiliary cruiser Komet while she was heading through the English Channel aiming for the Indian Ocean. Drayson on MTB 236 fired two torpedoes at Komet at a range of some 500 yards, setting her on fire. After an explosion, Komet sank with all hands. Drayson was awarded the Distinguished Service Cross for "great skill and bravery" and went on to command MTB 701.
In 1946, soon after leaving the Royal Navy, Drayson returned to Cambridge, where he gained a Blue for hockey and took a degree in History. After Cambridge, he became an assistant master at St. Lawrence College, his old school. From there he went to Felsted School as an assistant house master and in 1955 was appointed as head master of Reed's School, Cobham, Surrey. In 1964 he moved up to the headmastership of Stowe School, where he remained for fifteen years. In its obituary of him, The Daily Telegraph called Drayson the "head master of Stowe whose muscular Christianity and tireless persistence revived the school's fortunes".
One of Drayson's boys at Stowe was Richard Branson, who later confessed that while at the school "In a lengthy report, I instructed the then headmaster, R. Q. Drayson, in no uncertain terms just how I felt he should have been running the school. I covered many areas... Boldly, I said money would be saved by my plan and this could be put towards my next proposals." When the 16-year-old Branson left Stowe, Drayson told him, "Congratulations, Branson – I predict you will either go to prison or become a millionaire."
Always a committed Christian, after retiring from Stowe in 1979, Drayson spent some five years as lay chaplain to his wartime colleague Maurice Wood, Bishop of Norwich, after which the Draysons settled at Sandhurst, Kent. Drayson took an active part in village life until his death, on 15 October 2008, at the age of 89.
- Bob Drayson, Headmaster of Stowe whose muscular Christianity and tireless persistence revived the school's fortunes dated 26 October 2008 at telegraph.co.uk/news, accessed 13 December 2013
- Bob Drayson: headmaster of Stowe School (obituary) in The Times dated 22 October 2008
- Vincent P. O'Hara, The German Fleet at War, 1939–1945 (Google eBook; Naval Institute Press, 2013), p. 100
- Peter Charles Smith, Hold the Narrow Sea: naval warfare in the English Channel, 1939–1945 (1984): "According to contemporary British accounts, torpedoes from MTB236 (Sub-Lt R. Q. Drayson) hit and sank the merchant raider."
- Richard Branson, Screw Business as Usual (2011), p. 72
- "Richard Branson does it again: the flight of the floppy-haired super-entrepreneur". Evening Standard. 17 October 2013.
- The Church of England Year Book vol. 97 (1981), p. 117