Binge was born as Rhoda Cowell in Lamesley, County Durham, England, on 8 January 1913. She was the eldest of six children born to Andrew and Mary (née Scott) Cowell, who were married in 1912. She grew up on a farm before moving to London aged 15.
In 1936, aged 23, she married Albert Stanley Binge in Brentford, London. The couple was married for 46 years until Albert died in 1982 aged 70. They had one daughter, Yvonne, in 1940, and later moved to Netley, Hampshire, England, where Rhoda resided until her death in 2024 at the age of 111.
Binge has not been recognized in any news outlets for her longevity, but her grandchildren have celebrated her birthday on social media.
Her age was verified by Andrew Holmes, and validated by the ESO on 28 March 2023.