According to the Oxford Dictionary of English Surnames (Revised Edition), the surname originated at Springham Farm, Hellingly, Sussex.
Robert and Mary Springham appear to have married circa 1760 and had three sons and a daughter between 1764 and 1771. They were living at the old artillery ground when their daughter Mary was christened at St Leonards, Shoreditch in 1768. In 1786, the Old Bailey records show that Mary's mother was living at Baker's Row, Whitechapel. It also mentions that she had breakfast at her brother's. There was no mention of her father.