Ezra is a scion of the Ezra-Sassoon banking and trading dynasty. His ancestor, David Ezra, was a highly successful businessman in Calcutta, India. Another ancestor, David Sassoon, was treasurer to the Ottoman Empire in Baghdad before setting up in Bombay, now Mumbai, and becoming a British citizen. His mother, from Venice, Italy, was for many years a language coach at Glyndebourne Festival Opera.

Ezra was educated at Ampleforth College, where he was a contemporary of Julian Fellowes, and at the University of Westminster where he studied film production.

Ezra's horror movie, Slaughter High (1986) (originally April Fools Day), was picked up by Vestron at the Cannes Film Festival for ten times its production costs. He has directed several films, including Savage Hearts (1995), which featured Richard Harris, Julian Fellowes and Jerry Hall. Waking Ned Devine (1998), which he co-produced, was picked up by Fox Searchlight and grossed over $100 million. He wrote the screenplay for Steal (2002), which opened in the number 1 spot in France during the Cannes festival. His film House Swap (2010) won at the Los Angeles Cinema Festival of Hollywood.

He is married to Production Designer and Composer Jenny Chartres. He is the author of several books and plays for children. In the 1970s and early 1980s he acted in several BBC TV productions, including The Young Ones (1982) and The Grand Inquisitor (1976) with John Gielgud.