Sir Gawaine was raised at Leeds Castle in Kent, purchased by his mother, Lady Baillie, and her sister Dorothy Paget in 1928. Following the outbreak of World War II, five-year-old Baillie lived with his American cousins, the Whitney family, before returning to England after the war. He succeeded his father, Sir Adrian Baillie, 6th Baronet, to the family title on 8 January 1947, becoming the 7th Baronet of Polkemmet, Linlithgowshire. Baillie was educated at Sandroyd School, Eton, and Cambridge.
Sir Gawaine’s racing career began in 1956 with a Lotus Eleven sports car. By 1958, he had joined the Equipe Endeavour team, achieving a win at the John Davy Trophy at Brands Hatch in a Jaguar Mark 1 during the inaugural British Saloon Car Championship season.
In 1960, Sir Gawaine purchased a Lotus Elite and entered rounds of the World Sportscar Championship, including his first attempt at the 24 Hours of Le Mans. The following year, he competed in the Tour de France automobile competition, finishing second in the touring car category. In 1962, a crash during the same competition resulted in injuries after his Jaguar MkII fell 100 ft (30 m) down a hillside, leaving him with numerous cuts to his face.
Sir Gawaine returned to the British Saloon Car Championship in 1962, driving an American-built Ford Galaxie. He took the Galaxie to Australia in 1964, partnering with Lex Davison in the Sandown 6 Hour International. In 1965, he finished second in the class championship of the British Saloon Car Championship with a Ford Mustang, behind teammate Roy Pierpoint. He achieved a first-in-class finish at the 1966 British Saloon Car Championship with a Ford Falcon, benefiting from his expertise in supercharging.
During the 1962 Tour de France automobile competition, Sir Gawaine crashed his Jaguar MkII, falling 100 ft (30 m) down a hillside and sustaining numerous cuts to his face.
Sir Gawaine retired from racing in 1967, returning to his hobby of stamp collecting.
After retiring from motor racing, Sir Gawaine participated in sports car racing, including an attempt at the 24 Hours of Le Mans in 1960. He also competed in the Tour de France automobile competition in 1961 and 1962.
Sir Gawaine amassed one of the greatest collections of stamps of the former British Empire, almost entirely in secret. His goal was to build a comprehensive collection of Great Britain and British Empire postage stamps, from the earliest Queen Victoria issues to modern times. He focused on perfectly preserved stamps, acquiring over 100,000 stamps, including a copy of the scarce Edward VII 2d Tyrian plum. Sotheby’s described the collection as the most important to be sold in more than 50 years, dividing it into ten separate auctions which exceeded initial estimates by more than £4m.
In 1966, Sir Gawaine married Margot Beaubien, the daughter of Senator Louis-Philippe Beaubien of Montreal. They had a daughter, Liza (born 1969), and a son, Adrian (born 1973), who became Sir Adrian Louis Baillie, 8th Baronet, upon his father’s death.