One of the many Australians who came to Europe in the 1960s to pursue careers in motor racing, Bellamy first gained recognition for his work with Gordon Coppuck on the McLaren M14 in 1970. When Coppuck decided to concentrate on Indycars Bellamy became chief designer of the 1971 McLaren M19A. That year he also designed the McLaren M21 Formula 2 car which was raced in 1972.That year he was poached from McLaren by the new owner of Brabham Bernie Ecclestone and he revamped the Brabham BT34 as the BT37. Ecclestone then decided to hand over design to Gordon Murray and Bellamy moved to Team Lotus for which he designed the 1973 Formula 2 car which was run in Texaco Star colors for Emerson Fittipaldi and Ronnie Peterson. He then became increasingly involved in Formula 1 design work and was one of the team (alongside Colin Chapman, Peter Wright and Martin Ogilvie) which produced the famous Lotus 78, the first car to feature ground-effect aerodynamics. He was lured away to Fittipaldi Automotive in 1978 but his Fittipaldi F6 in 1979 was not an effective machine and at the end of the year he moved on, joining up with Nigel Bennett to design an Ensign for the 1980 season.Bellamy moved to March Engineering in April 1981 to join Gordon Coppuck's Indycar design team. He then turned his attention to designing March Formula 2 cars. They were very effective but Ralt-Hondas proved to be the dominant force. When the F2 series was canceled and replaced by Formula 3000 Bellamy designed the March 85B with which Christian Danner became the inaugural F3000 champion. That year he left March and worked as a consultant engineer with Interscope Racing in the United States. In 1986 he was hired by rival Lola, designed the Lola Formula 3000 chassis and then worked with Eric Broadley on the Lola F1 design which was run by the Larrousse Calmels team. He stayed at Lola until midway through 1988 when he fell out with Broadley. He returned to March where he designed the Formula 3000 chassis for 1989, leaving Coppuck free to work on the March F1 program.In 1993 Bellamy retired to Australia but was still involved in the Australian Touring Cars Championship and later as chief engineer with Team Schuppan in sportscar racing.