Witchell was born in Shropshire and studied law at the University of Leeds, where he edited the student newspaper. He has worked for the BBC since 1976. He reported from Northern Ireland and the Falkland Islands during the 1982 Falklands War. Witchell, along with Sue Lawley, then became the first newsreader of the BBC's Six O'Clock News when that programme was launched in 1984. In 1988 Witchell famously grappled with a group protesting against Britain's Section 28 (against the promotion of homosexuality in schools) who had invaded the studio during a live broadcast. He is said to have sat on one woman.

The following year he moved from the evening to breakfast news slot, a role he filled for five years. In 1994 he left the studio to become a reporter for factual affairs programme Panorama. During this period he was also the first to report the death of Diana, Princess of Wales.

In 1998, Witchell became a royal and diplomatic correspondent. In 2002, his obituary of Princess Margaret, recorded some time before her death but screened immediately after the announcement of her death, provoked controversy, as it mentioned her lovers and love of whisky. Witchell provoked royal ire again in 2005. Whilst at a press conference at the Swiss ski resort of Klosters, Witchell asked Prince Charles how he and his sons were feeling about his forthcoming marriage to Camilla Parker Bowles. After a response from his son William, Charles said under his breath, and referring to Witchell, "These bloody people. I can't bear that man. I mean, he's so awful, he really is." Witchell himself was then in the headlines. The BBC defended their reporter saying "He is one of our finest. His question was perfectly reasonable under the circumstances." The outburst even brought praise from rival broadcasters, Sky's Geoff Meade praised Witchell, describing him as one of the most respected and least irreverent of all the media present. A BBC Radio 5 phone poll on the day did, however, indicate greater support for the Prince than for Witchell, with approximately 1000 out of 1700 votes going to 'Charles' over 'Nick'.

Witchell is also the author of a book about his failed search to find the Loch Ness monster.