Joseph Charles Barrow was the son of Charles Barrow, of Barrow & Smith, linseed oil merchants of Upper Thames Street in London. By 1771 his father had moved the family to Fulwell Lodge in West Twickenham. Here he started a seed-crushing business using the adjacent mill on the River Crane.
Joseph Charles did not follow in his fathers business: He took up art and was engaged as an assistant in 1791 by Henry Pars at his drawing school in the Strand. He is noted as exhibiting at the R.A. between 1789 and 1802. He produced a number of views of Strawberry Hill for Horace Walpole.
He opened his own drawing school in 1792 at 12 Furnival Court, Holborn where he gave evening classes in drawing twice a week. John Varley (1787-1842) is noted for studying there in 1793. Subsequently, Barrow took Varley on a sketching tour to Peterborough from which he emerged as a professional painter.