Acton's grandfather, who in 1791 succeeded to the baronetcy and family estates in Shropshire, previously held by the English branch of the Acton family, represented a younger branch which had transferred itself first to France and then to Italy. However, by the extinction of the elder branch, the admiral became head of the family. His eldest son, Richard, married Marie Louise Pelline, the only daughter and heiress of Emmerich Joseph, 1st Duc de Dalberg, a naturalised French noble of ancient German lineage who had entered the French service under Napoleon and represented Louis XVIII at the Congress of Vienna in 1814. After Sir Richard Acton's death in 1837, she became the wife of the 2nd Earl Granville (1840). Marie Louise Pelline de Dalberg was heiress of Herrnsheim in Germany. She became the mother of John Dalberg-Acton who was born in Naples.
From an old Roman Catholic family, young Acton was educated at Oscott College under Dr (afterwards Cardinal) Wiseman until 1848 and then at Edinburgh where he studied privately. At Munich, Acton resided in the house of Johann Joseph Ignaz von Döllinger, theologian and forerunner of the Old Catholic Church, with whom he became lifelong friends.