After being educated at the Carlisle grammar school, and acquiring skill in fencing and music, Story read law under Dr. Richard Gilpin at Scaleby Castle, Cumberland.
He at once ‘put off his usual airs, his jovial address, and the sword which he had worn as a modish and manly ornament.’ He also burned his musical instruments, and divested himself of the superfluous parts of his apparel.
That year he first met William Penn, who, on his deciding to settle in London (1695), assisted him to find legal employment among the Quakers, in conveyancing and drawing up settlements.
He was appointed registrar of the Society of Friends, and employed to abstract and index the deeds of London quarterly meeting.
At this time he paid visits to, and discussed Quakerism with, the Countess of Carlisle, Sir John Rhodes of Balbur Hall, Derbyshire; Sir Thomas Liddell of Ravensworth Castle, Northumberland; and the Tsar Peter the Great, then on a visit to Greenwich, whom he presented the Latin version of Robert Barclay's Apology.
At Kilkenny Story was arrested, but after a few days the sheriff released him, in spite of the bishop of Ossory having committed him for three months' imprisonment.
From this time he paid during the season frequent visits to Bath, where his preaching was so admired that the afternoon meetings were crowded.
He devised by his will, dated 1741, all his lands in England and Pennsylvania to be sold, the former for the benefit of his sister, Ann Elliot, and her two daughters; the latter for members of the Shippen family.