He was the only child of Ernest Leonard Redhead, a silk screen printer and advertising agent, and his wife, Janet Crossley (née Fairley).

After being passed over for the editorship of The Guardian in favour of Peter Preston in 1975, he left to join the Today programme on BBC Radio 4, replacing Robert Robinson.

He was already an experienced broadcaster, having been 'discovered' around 1960 by a BBC Manchester producer, Olive Shapley, who was looking for a presenter of a television programme called Something to Read:I held auditions over two days and there were some promising people.

However, on the second day a young man turned up who was clearly highly intelligent and knowledgable[sic], oozed confidence, communicated effortlessly through the camera, was very funny and never stopped talking.

[8]Later, Redhead presented Points North on television, and chaired the Saturday night Radio 4 topical conversation programme A Word in Edgeways for many years.

[11] During his time on the Today programme, Redhead was accused of political bias by Conservative Chancellor Nigel Lawson, and in reply enquired "Do you think we should have a one-minute silence now in this interview, one for you to apologise for daring to suggest that you know how I vote and secondly perhaps in memory of monetarism which you have now discarded?"

However, Redhead claimed to be more of a Tory wet, not a socialist, and stated that he had cast a personal vote for Macclesfield's Conservative MP, Nicholas Winterton.

The death of Redhead's youngest son, William, in a car crash in France in 1982, aged 18, led him to rediscover religious faith, and he became a confirmed member of the Church of England a few months later.