Brennan was born as Joan Edith Lewis in Finchley, London, England, on 10 March 1912. Her father, Henry William Lewis, was wounded during the Battle of the Somme in 1916, later succumbing to his injuries on 4 May 1917 aged 39. Brennan remembered her father taking her and her sister to a pantomime in December 1916, which would be the last time she saw him.

Brennan’s mother, Edith Mary (Dart) Lewis, lived to be 95 years old. After her father’s death, the family were very poor, and emigrated first to Australia before settling in New Zealand around 1922. Brennan trained as a Karitane nurse, and loved looking after children.

On a voyage back to England in 1934, Brennan met her husband, Thomas George “Tom” Brennan, and the pair were married in October 1937. They emigrated to Hawke’s Bay, New Zealand, and had three children. During World War II, Tom Brennan worked as a telegraphist and lighthouse keeper, and they enjoyed spending time together fishing.

After the war’s end, the couple moved to Auckland, residing in Campbell’s Bay for 36 years before moving to Selwyn Village, an Auckland residential care facility, in 1990. Brennan’s husband died in 1998 aged 89.

Until the age of 107, Brennan lived independently, growing her own vegetables and taking the bus to go shopping. She died of a chest infection on 29 July 2022 at the age of 110 years, 141 days. She is, as of 2023, the oldest person ever to die in Auckland.