Curry was born on 9 September 1949 in Birmingham, England. He was educated at Solihull School, an Independent School in the West Midlands followed later by St Andrews, an independent boarding school in Somerset. As a child, Curry wanted to become a Dancer, but his father disapproved of dance as an activity for boys, so instead, at the age of 12, he began to take figure skating lessons under the guidance of Ken Vickers at the Summerhill Road rink in Birmingham.
For the first several years, Curry's involvement with skating was rather Casual. Curry's father died when he was 15; he then moved to London to study with Arnold Gerschwiler, who coached him to his first British title in 1971. In 1972, Curry found an American sponsor who enabled him to study in the United States with Gus Lussi and Carlo Fassi.
Prior to the 1976 World Championships, Curry was outed as gay by a German tabloid newspaper, Bild-Zeitung. It caused a brief scandal in Europe at the time, but Curry's sexual orientation was generally ignored by the press and public for many years afterwards.
Curry's Broadway theatre credits include Icedancing (1978) as a performer and Director and the 1980 revival of Brigadoon as an actor and the Roundabout Theatre 1989 revival of Privates on Parade as an actor.
In 1987 Curry was diagnosed with HIV, and in 1991 with AIDS. Before his death, he spoke openly to the press about both his disease and his sexual orientation. He spent the last years of his life with his mother. He died of an AIDS-related heart attack on 15 April 1994 in Binton, Warwickshire; he was 44 years old.
A 2007 biography of actor Alan Bates claimed that Curry and Bates had a two-year affair, and that Curry died in Bates's arms.
In 2018, a documentary on Curry's life and career, The Ice King, was released by Dogwoof Pictures.
