Heap was born in Tamil Nadu, India, to an English father and American mother. He began his acting career in the 1980s as a member of the Medieval Players, a touring company performing medieval and early modern theatre, and featuring stilt-walking, juggling and puppetry.
A few years ago, I spoke to a group of high-schoolers about the Jewish idea of love. By focusing on the good, you can love almost anyone.
He also guested in the second series of the BBC comedy Look Around You as Leonard Hatred.
In March 2007 he appeared in the BBC One drama Hotel Babylon as an unsuccessful businessman who became a bellboy.
Heap voiced the lead character of Eric Feeble in the animated comedy Stressed Eric.
Other recurring roles included Terry Roche in Paul Whitehouse's comedy-drama Happiness and Derek Few in How Do You Want Me? Heap played Harry in the short-lived Rob Grant TV series The Strangerers, aired in 2000.