Born on 15 March 1789 at Polperro, he came of staunch Methodist stock. He trained as a doctor at Guy's and St. Thomas's hospitals in London, before returning to his native Polperro to maintain a lifelong medical practice there. He was also a keen naturalist, particularly in marine biology, made many contributions to scientific journals and wrote A History of the Fishes of the British Islands (1862). He was also an antiquarian and wrote a History of Polperro, published posthumously in 1871.
His family had been Methodists since the 1760s. Jonathan supported Samuel Warren and in 1837 led the society in the village into the Wesleyan Methodist Association, building a chapel in the following year. He died at Polperro on 13 April 1870. A memorial originally in the chapel is now in the garden of his former home by the Saxon Bridge.
He makes occasional appearances in the writings of his grandson, Sir Arthur Quiller-Couch, e.g. as 'Doctor Unius' in Corporal Sam and Other Stories.
Although his parents had become Anglicans, Quiller-Couch's Methodist ancestry may well explain why he chose to write his novel Hetty Wesley, which upset many Wesleyans of the day by its sympathetic presentation of Hetty.