Gunn spent more than 20 years of her career as a political journalist, including 12 at The Times.
In 1995, Gunn was appointed political press secretary to the then prime minister, John Major, and remained in that role until his defeat at the 1997 general election.
He made Gunn an MBE in his 1997 resignation honours list.
Following her stint as Major’s press secretary, Gunn worked at FleishmanHillard and was a PRCA trainer covering public affairs.
Francis Ingham, PRCA director general, said: "Sheila was a personal friend. She was also that rare thing – politically astute, yet also with a lovely soul. Those she trained always commented not just on her skill, but also on her kindness. She will be missed."
Gunn’s career also saw her take a place as a visiting lecturer at City University where she taught journalism for 14 years.
She also served as a Conservative councillor in Camden when she was elected to Belsize ward in 2002.
Kevin Maguire, the Mirror’s political editor, said in a tweet: "Very sorry Sheila Gunn's died, ex-Times hack and John Major's spokeswoman. Really decent and always had a smile. RIP."
Paul Waugh, the editor of the Politics Home website, also tweeted: "Sad to hear of the death of Sheila Gunn, John Major's former press aide and all-round good egg."