Heeley was born in Staffordshire, England and began his career as an apprentice designer at the Royal Shakespeare Theatre in 1948, and soon established himself as an important designer at that theater and at Sadler's Wells Theatre in London.

He also designed sets and costumes for several Broadway productions and at the Metropolitan Opera.

[1] He also taught design at the Tisch School for the Arts at NYU, as well as other universities in the United States, England and Canada.

He was notably the first designer to win Tony Awards for both sets and costumes for the same production with his work on the Royal National Theatre production of Rosencrantz and Guildenstern Are Dead in 1968.

[3] In 2013, he received The Robert L. B. Tobin Award for Sustained Excellence in Theatrical Design,[3] as well as the USITT Distinguished Achievement Award for his work in costume and scenic design.