He was educated at Haydon Bridge school, and admitted sizar at St John's College, Cambridge, on 4 July 1774.
His father's means were insufficient for the complete education of his son, and the cost of his residence at college was borne by a titled lady of Northumberland who discovered his talents, but in 1778 she cut off her contributions.
In London he in fact concentrated on journalism, and after appearing as counsel in a few contested election petitions, gave up the legal profession.
While connected with the Post he fought a duel in Hyde Park with Sir Henry Bate Dudley, and was wounded in the right arm.
His comedy, The Fugitive, was brought out at the King's Theatre in the Haymarket by the Drury Lane Company with success on 20 April 1792, and, when printed, passed through three editions.
Richardson also wrote the prologue to the Glorious First of June, the after-piece which was acted at Drury Lane on 2 July 1794 for the benefit of the widows and children of the sailors who died at the naval battle of that name.
One night he remained in the House of Commons until five o'clock in the morning to record his vote in the small minority with Charles James Fox.
He published for his party in 1787 an anonymous pamphlet, called The complete Investigation of Mr. Eden's Treaty, which embodied reputable commercial statistics.