Born Marguerite Anne Harvey on 18 May 1792, she was baptised on 29 May 1792. In later life she Anglicized her name to Margaret Ann.

As a child, Neve survived a fall down the stairs, which left her concussed for three days. Neve could remember the turmoil that the French Revolution brought to Guernsey. In 1807, Neve set sail for Weymouth with her father, but a storm caused the ship to land at Chesil Beach. She was educated in Bristol, England, gaining an interest in literature and poetry. Neve met with Charles François Dumouriez, a general of the French Revolutionary Wars, who dubbed her la spirituelle. She married John Neve in St. Peter Port, Guernsey on 18 January 1823 and took up residence in England, but returned to Guernsey in 1849 after he committed suicide.

Neve travelled abroad to various countries with her sister, who died aged 98. Their last trip was in 1872, when they visited Krakow (then in Austria-Hungary, now in Poland). Her mother lived to the age of 99. She was the oldest living person before her death at age 110 years, 321 days; dying peacefully on 4 April 1903. She was one of the few people to have lived during the 18th century, 19th century, and the 20th century.