Born in a farming family at Low Ham in the Somerset Levels, Sherrin attended Sexey's School, in Bruton, Somerset. Although he read law at Exeter College, Oxford and subsequently qualified as a barrister, he became involved in theatre at Oxford and joined British television at the founding of independent television in 1956, producing shows for ATV in Birmingham.

Sherrin joined the BBC in 1957 as a temporary production assistant, then began working for them as a producer in "Television Talks" in 1963. Specialising in satirical shows, he worked extensively in film production and television.

In 1962 he was responsible for the first satirical television series That Was The Week That Was starring David Frost and Millicent Martin and its successors Not So Much a Programme, More a Way of Life and BBC-3. His other shows and films included Up Pompeii!, Up the Front, The Cobblers of Umbridge and The Virgin Soldiers. In 1978, he also hosted We Interrupt This Week, a lively and humorous news events quiz featuring two teams of well-known journalists and columnists sparring against one another. The show was a production of WNET/Channel 13 New York.

Sherrin produced and directed numerous theatre productions in London's West End, including Jeffrey Bernard is Unwell and the landmark musical Side By Side By Sondheim. He received an Olivier Award in 1984 for directing and conceiving The Ratepayers' Iolanthe, an adaptation by Sherrin and Alistair Beaton of the Gilbert and Sullivan opera Iolanthe.

On BBC Radio 4, from 1986, he presented a light entertainment show on Saturday mornings (latterly evenings) called Loose Ends, and Counterpoint, a quiz show about all types of music, until forced off the air when his voice succumbed to throat cancer.

He also toured the UK with his one man show An Evening of Theatrical Anecdotes.

Sherrin wrote two volumes of autobiography, several books of quotations and anecdotes, as well as some fiction; and several works in collaboration with Caryl Brahms.

Openly gay, he was a patron of the London Gay Symphony Orchestra. Sherrin was awarded a CBE in the 1997 New Year’s honours list.He was diagnosed with unilateral vocal cord paralysis in January 2007 and died of complications of throat cancer on 1 October 2007, aged 76.