Branston was the son of a general copper plate engraver and heraldic painter, born at Lynn, Norfolk in 1778.
He soon became the head of his profession in London, where nothing equal to Thomas Bewick and his pupils had been produced before his arrival.
The 'Cave of Despair,' after Thurston, in William Savage's Practical Hints on Decorative Printing, 1822, is generally considered his best plate,[2] and shows his skill both in 'white' and 'black' line.
Amongst the works illustrated in whole or in part by him were edition of David Hume's The History of England published by Wallis and Scholey, 1804–10; Robert Bloomfield's Wild Flowers, 1806; and poems by George Marshall, 1812.
Branston projected a volume of fables in rivalry with those of Bewick after designs by Thurston, but after a few of them were cut he abandoned the enterprise.