Roy was born in London, the son of a Scottish dentist. He was educated at St Paul's School, London, and the Royal Military College, Sandhurst, Urquhart was commissioned into the Highland Light Infantry in 1920. When stationed in Malta with his battalion, he became a friend of the actor David Niven, who recalled Urquhart in his autobiography The Moon's a Balloon, describing him as "a serious soldier of great charm and warmth" (both were commissioned in Highland Light Infantry - Urquhart in 1920 and Niven in 1930). Urquhart attended the Staff College, Camberley from 1936 to 1937.
Urquhart was serving in India during the early years of the Second World War. He remained there until 1941, when he was posted to North Africa before an appointment as a staff officer in the 3rd Infantry Division, serving in the United Kingdom. Thereafter, his career accelerated. Between 1941 and 1942 he was promoted to lieutenant colonel and commanded the 2nd Battalion, Duke of Cornwall's Light Infantry until 1943, when he was appointed as a staff officer in the 51st (Highland) Infantry Division, which was then stationed in North Africa and commanded by Major General Douglas Wimberley. For a short time, he commanded the 231st Infantry Brigade Group, which saw action in the Allied invasion of Sicily, later the Allied invasion of Italy, before returning to England.
Until 1944, Urquhart was a senior staff officer in XII Corps. However, in that year, he was given command of the 1st Airborne Division. Its former commander (Major-General George F. Hopkinson) had been killed in the early stages of the Italian Campaign, and his successor, Brigadier Ernest Down had been given command of the 44th Indian Airborne Division in India. Ironically, Urquhart was prone to airsickness and had never commanded or, for that matter, been a member of an airborne unit. Although a newcomer to airborne operations, Urquhart commanded his division during Operation Market Garden in September 1944 as it was dropped into Arnhem in the Netherlands in an attempt to secure a crossing over the River Rhine. For nine days Urquhart's division fought unsupported against armoured units of II SS Panzer Corps. Suffering increasingly heavy casualties, the British airborne forces desperately held on to an ever-shrinking defensive perimeter until orders were received for the remnants of the division to withdraw across the Rhine on 25 September. During these nine days of heavy fighting the 1st Airborne Division had lost over three-quarters of its strength. Shattered as a fighting formation, the division was withdrawn to the United Kingdom and saw no further action in the Second World War. Urquhart was awarded the Dutch Bronze Lion for his command. It is rumoured that Urquhart assaulted and knocked out Lieutenant-General Frederick "Boy" Browning on his return from Arnhem after Browning made some inappropriate remarks about the Arnhem battle, but no official record of this incident exists in military records (source: an officer serving under Urquhart witnessed the event).
In May 1945, following the German surrender, Urquhart led a reconstituted 1st Airborne Division as the advanced guard of Force 134 in Operation Doomsday, the Allied occupation of Norway. During its time in Norway, the division was tasked with supervising the surrender of the German forces, as well as preventing the sabotage of vital military and civilian facilities. Due to delays in troop arrivals, Urquhart ended up driving into Oslo in a captured German staff car, accompanied only by four military policemen and two platoons from 2nd Battalion, South Staffordshire Regiment. Until the arrival of other units from Force 134, as well as the Headquarters of Allied Forces, Norway, Major General Urquhart and his headquarters staff had complete control over all Norwegian activities. This meant that it was Urquhart who welcomed Crown Prince Olaf of Norway and three ministers representing the Norwegian Government when they arrived on a Royal Navy cruiser. General Thorne arrived on 13 May to take command of all Allied troops in Norway and at the end of August, 1st Airborne Division returned to the United Kingdom and disbanded. Urquhart was rewarded with the Norwegian Order of St Olav.
Following the end of the war Urquhart served in several staff positions, including service as the General Officer Commanding Malaya (1950–1952) during the Malayan Emergency. He also commanded the 16th Airborne Division, a Territorial Army (TA) formation, from 1947 to 1948, then the 51st/52nd Scottish Division until 1950. Urquhart retired from the army in 1955.
After leaving the British Army Urquhart became an executive in the heavy engineering industry, retiring in 1970. In 1958 Urquhart published Arnhem: Britain's Infamous Airborne Assault of World War II (ISBN 0-9644704-3-8) detailing his exploits in the battle.
Urquhart was portrayed by Sean Connery in the 1977 film A Bridge Too Far, for which he himself served as a military consultant. Despite his earlier-mentioned friendship with David Niven, in a publication about the making of the film, he was quoted as saying that he wasn't much of a film fan himself and could not understand why his daughters were so excited at Connery's selection to play him.
He is the subject of the biography Urquhart of Arnhem (ISBN 0-08-041318-8) by John Baynes.
Urquhart and his wife Pamela had four children, among them Elspeth Campbell (wife of the former leader of the Liberal Democrat party Menzies Campbell) and Suki Urquhart, author of The Scottish Gardener.
In his memoirs, Campbell says that Urquhart told Elspeth's first husband, Philip Grant-Suttie, "there's no need to be formal; just call me General", and that he also insisted on tasting all the food and champagne for Elspeth and Menzies' wedding before paying for it. He is also known to have told his daughter never to trust men who bought half-bottles of wine; Campbell bought Elspeth a full bottle on their first date.
Major General Urquhart died on 13 December 1988, aged 87 years.