Robert Hurrell Froude, then rector of Dartington, encouraged him to pursue painting as a profession, and supported him during studies at the Royal Academy.
Another large picture, representing the 'Delivery of the Tables of the Law to Moses on Mount Sinai,' was presented by him to Christ's Hospital in 1835.
A picture, painted at Rome in 1821, the 'Vision of the Chariots to the Prophet Zechariah,' was by permission of Pope Pius VII exhibited in the Pantheon.
In 1824 he made an excursion to the Alps for the purpose of investigating the route of Hannibal, and the idea of publishing Illustrations of the Passes occurred to him.
The work, containing 109 engravings, was issued in twelve parts, from 1827 to 1829, forming when complete two royal quarto volumes, and was dedicated to his earliest patron, Archdeacon Froude.
His next work, published in folio in 1842-4, was Italy, Classical, Historical, and Picturesque, illustrated and described, with sixty engravings from drawings by himself, Eastlake, Prout, Roberts, Stanfield, Harding, and other friends.
Letitia Elizabeth Landon published a poem on the subject of Brockedon's painting of Raphael Showing his Mistress her Portrait in The Literary Gazette in 1824.
In 1843 he patented an invention for the manufacture of wadding for firearms; another for compressing sodium carbonate and potassium carbonate into the form of pills and lozenges;[3] and for preparing or treating plumbago by reducing common black lead to powder, and then compressing it in vacuo, so as to produce artificial plumbago for lead pencils purer than any that could then be obtained, in consequence of the exhaustion of the mines in Cumberland, and especially valuable to artists because it was free from (diamond) grit.
The invention was first worked for him by Messrs. Mordan & Co., but at his death in 1854 the plant and machinery were sold by auction, and bought by one of the merchants connected with the lead industry at Keswick.
The son, who was educated as a civil engineer, became the favourite pupil of Isambard Kingdom Brunel, but died of consumption at the age of 28, on 13 November 1849.