Prior to becoming a television writer, Boucher had worked at Calor Gas as a management trainee and he also gained a Bachelor of Arts in Economics at the University of Essex.

In science fiction, he wrote three Doctor Who serials in the late 1970s: The Face of Evil, The Robots of Death and Image of the Fendahl. Perhaps his most durable contribution to Doctor Who mythology was the creation of Leela, the savage companion played by Louise Jameson. Boucher was commissioned for the programme by Robert Holmes, who would suggest that Boucher be appointed as script editor of new science fiction series Blake's 7. He served in this role for the entirety of its four season run from 1978 to 1981, also writing several episodes himself, including the well-remembered final episode. In 1987 he created his own series Star Cops, which combined the science fiction and crime genres, and lasted only nine episodes.

In the genre of police dramas, between working on Doctor Who and Blake's 7, Boucher was the script editor on the second season of the drama Shoestring, which followed the investigations of private detective and radio show host Eddie Shoestring. In 1982, following the end of Blake's 7, Boucher script edited and wrote for the third season police drama Juliet Bravo. He later moved on to script edit the detective show Bergerac, working on the programme throughout the 1980s.

All of the above television programmes were produced in-house by the BBC and broadcast on the BBC One network, with the exception of Star Cops which was shown on BBC Two. For the ITV network, he briefly contributed to Thames Television's police drama The Bill during the mid-1980s.

More recent work has included several Doctor Who novels for BBC Books, all featuring the character of Leela, and a series of straight-to-CD full-cast audio dramas entitled Kaldor City, which combine elements from his Doctor Who serial The Robots of Death with his Blake's 7 work.

Boucher is an atheist. He disapproves of the introduction of religion into government policy and the education of children.

In October 2004, Boucher gave an interview in which he revealed his support for trade unions and the traditional values of the Labour Party :

“I was and remain "Old Labour" and an unrepentant supporter of unions in principle and in practice. On the day when no worker needs the help and protection of other workers against unconcerned and/or rapacious employers I will cheer myself hoarse. Since I don’t believe in an afterlife however I can say with absolute certainty I shall never see that particular dawn.”

He also described former Prime Minister of the United Kingdom Margaret Thatcher as “horrendous” and her followers as a “carpet-bagging gang of loathsome thugs and conmen”.