McClure was born as Edna Lyon in Blackley, a suburban area of Manchester, England, on 28 August 1899 as the eldest child of James Alfred and Amy (née Hulme) Lyon. She had two brothers: Alfred and James. Her father worked as a clerk at a cloth warehouse. Her paternal grandmother, Hannah Lyon, lived to be a centenarian, dying in 1952 aged 101.

McClure married her husband, locomotive cleaner Walter McClure, in 1922. The couple had two children: Beryl in 1930, and Glenys in 1942. By 1939, her husband was working as an aircraft storekeeper, and McClure herself was working as a cinema kiosk attendant before becoming a nurse.

In 1967, McClure was widowed; she also outlived both of her daughters, who died in 1989 and 2001 respectively. As a centenarian, she had vivid memories of the Titanic, World War I, and the Great Depression. She lived independently until the age of 105, when she moved into a nursing home in Blackley.

McClure never smoked, but enjoyed the occasional glass of sherry. She died on 11 January 2010 at the age of 110 years, 136 days, in the same Manchester hospital she was born in. She was survived by three grandchildren, six great-grandchildren and an unreported number of great-great-grandchildren.