He was educated at Oundle School and later read Drama at Manchester University. After a brief career as a journalist, he began writing dramatic works in 1971. After becoming prominent for the BBC production of his adaptation of Charles Dickens's novel Nicholas Nickleby, which also aired on American public television, he became best known for his original plays, which deal overtly with political subjects, many of which have premiered at the Royal Shakespeare Company. In 1975 he received the John Whiting Award for his play Destiny. His overtly-political original dramatic works include include a trilogy of plays on the theme of negotiation set in Eastern Europe: The Shape of the Table (1990), written shortly after the collapse of the Soviet Union; the second part, Pentecost, set during the early 1990s, concerning the discovery of a mural in a small church; and The Prisoner's Dilemma (2001), which premiered shortly before September 11.
His other recent overtly-political plays include Albert Speer (2000) and Playing with Fire (2005), both of which premiered at the Royal National Theatre, in London. Albert Speer, based on Gitta Sereny's biography Albert Speer, about Adolf Hitler's chief architect, munitions minister, and friend Albert Speer, and other historical biographies and documents, focuses on Speer's imprisonment, release, and personal struggle to overcome his denial of the Holocaust. Playing with Fire, a play about the politics of New Labour, multiculturalism, and ethnic tensions in the North of England, has been produced both on stage and in an adaptation for radio.
In 2003 Edgar was commissioned by the Oregon Shakespeare Festival, in Ashland, Oregon, and the Berkeley Repertory Theatre, in Berkeley, California, to write Continental Divide, a two-play epic about American politics, which was produced at both theatres to mixed reviews.