She was born at Briton Ferry in Glamorgan to Charles Pegge, a doctor who ran Vernon House, the last privately owned asylum in Wales. One of seven children, Cunnington's older brother Edward followed his father as a doctor, and was also a notable rugby player and Welsh international. Maud was educated briefly at Cheltenham Ladies' College. In 1889, she married Ben Cunnington who was the honorary curator of Devizes Museum. Their only son, Edward, was killed in the First World War.
From 1897, Maud carried out early Rescue archaeology work during development in the area but also carried out full excavations at some of the most important sites in British archaeology. These included the first known Neolithic causewayed enclosure at Knap Hil, the Iron age village at All Cannings Cross, West Kennet Long Barrow, Figsbury Ring, Woodhenge, (which she named) and the The Sanctuary. This last monument she rediscovered as it had been lost since William Stukeley saw it in the eighteenth century. Woodhenge and The Sanctuary were bought by the Cunningtons and given to the nation. In 1931, she was elected president of the Wiltshire Archaeological and Natural History Society.
In 1948 she was made CBE for services to archaeology, the first woman archaeologist to receive the honour. Bedridden since 1947, and suffering from Alzheimer's disease however, she never knew of the accolade. When she died at home a few years later she left almost all her property (£14,000) to Devizes Museum, (now Wiltshire Heritage Museum) allowing a salaried curator to be appointed for the first time. Her husband had died a few months previously.