Thompson trained at the Sadlers Wells Ballet School in London, and began his performance career at Covent Garden Opera Ballet. He became a soloist with American Ballet Theatre in 1960, and went on to work with Robert Joffrey at the Joffrey Ballet in 1967 in the capacity of ballet master.
"Basil brought joy, vigor, and dedication to his work as a ballet master, teacher, and coach," said Gerald Arpino, co-founder with Joffrey of the Joffrey Ballet and the company's current artistic director. "He knew the art of ballet thoroughly and lovingly shared it with all of us."
Thompson became the ballet master of the Milwaukee Ballet in 1981, and the company's artistic director in 1995. In 2000, he joined the faculty of the University of Iowa, from which he was on sabbatical when he died.