She was born on 25 March 1625 in the parish of St Olave Hart Street, London, to Sir John Harrison of Hertfordshire and Margaret Fanshawe, and had three brothers and a younger sister. Her childhood was spent in London and at Balls Park, Hertford. She liked not only French, needlework and music, but riding and running, and described herself with hindsight as "what we graver people call a hoyting girle." Her mother died in July 1640, and her father remarried, having a son and a daughter by his second wife.
Both her husband's and her own family were Royalists. In 1644 she married at Wolverton near Oxford her second cousin, Richard (later Sir Richard) Fanshawe (1608–1666), secretary of war to Prince Charles. They had 14 children, of whom four daughters and a son survived into adulthood.
They spent the latter years of the Civil War and the Interregnum travelling, for instance to Caen, Paris, The Hague, Ireland, Madrid, and Flanders, as well as London, Yorkshire, Huntingdonshire, Hertfordshire and Bath. Richard Fanshawe published translations and kept in touch with the royal family. The family joined Charles II in Flanders, Fanshawe was appointed Latin secretary and master of requests, and knighted at Breda. After the Restoration, he represented the University of Cambridge in Parliament, went to Portugal to help broker Charles II's marriage to Catherine of Braganza, and served as ambassador to Portugal (1662–63) and to Spain (1664–66). He died in 1666 in Madrid and his widow and her family returned to England. Ann petitioned the government for the payment of monies due to her husband, but with only partial success. She died in 1680, probably at Ware, Hertfordshire, where she was buried on 20 January 1680.
There is a portrait in oils of Lady Fanshawe by Cornelis Janssens van Ceulen held at the Valence House Museum in Dagenham, London, a gift from a descendant in 1963.
Ten years after her husband's death, Fanshawe wrote in 1676 the manuscript Memoir of him (today held in the British Library) for private family circulation. It was addressed to their son Richard and began with conventional biblical and other admonitions. It is interspersed with descriptions of Richard Fanshawe's character as one for his son to emulate, it provides a colourful account of their adventures, and carefully observed details of clothing and customs encountered in their travels. It was also intended to vindicate the family's financial claims against the government. It ends abruptly in 1671. There is a modern edition of the Memoir.
A book of cookery and medicaments compiled by Lady Fanshawe has also survived. The earliest entries, by an amanuensis, date from 1651. Her recipe for ice cream is thought to be the earliest recorded in Europe. . Her recipe for Sugar Cakes is: "Take 2 pound of Butter, one pound of fine Sugar, the yolkes of nine Egs, a full Spoonfull of Mace beat & searsed [sifted], as much Flower as this will well wett making them so stiffe as you may rowle it out, then with the Cup of a glasse of what Size you please cutt them into round Cakes & pricke them and bake them."