Edwards, the elder son of a chairmaker and carver, who had come from Shrewsbury, and settled in London, was born in London 7 March 1738. He was a weakly child, with distorted limbs, and remained of very small size all his life. At an early age he went to a French Protestant school, but at fifteen was removed in order to work at his father's business.
He worked up to eighteen with a Mr. Hallet, an upholsterer at the corner of St. Martin's Lane and Long Acre, drawing patterns for furniture. His father then sent him to a drawing school, and in 1759 he was admitted as a student into the Duke of Richmond's gallery. He lost his father in 1760, when the support of his mother and sister devolved upon him. Edwards took lodgings in Compton Street, Soho, and opened an evening school for drawing.
He lost his mother in 1800, but continued to support his sister until his death, at the age of 68. He was buried in St. Pancras churchyard. Edwards was a proficient in etching, and in 1792 published a set of fifty-two etchings. There is a volume in the print room of the British Museum containing others, and also some of his unsuccessful essays in that art. He designed numerous illustrations, wrote verses, and played the violin.