Born in Trinadad, the great-grandchild of Chinese immigrants, Dai moved to London as a teenager to study ballet and modern dance. Her teachers included Anton Dolin, Margaret Craske, Marie Rambert, and Kurt Jooss.
After World War II began in 1939, London's China Institute offered to send Dai and other students to China; she accepted, despite speaking no Chinese.
In China, Dai did research on the country's folk traditions before holding a series of leadership positions in its national dance institutions. She founded the Beijing Dance Academy in 1954, and led the Experimental Ballet Troupe, later the Central Ballet of China and now the National Ballet.
During the Cultural Revolution of the 1960s and '70s, she was removed from her post with the Central Ballet and assigned to do manual labor. She returned as artistic advisor in 1978 and accompanied the company when it made its New York debut in 1986.