Cleveley was born in Southwark. He was not from an artistic background, and his father intended him to follow the family trade of joinery, so he set up as a carpenter or shipwright in around 1742 at the Deptford Dockyard. Continuing his work in that area throughout his life (indeed, he is referred to as ‘carpenter belonging to His Majesty’s Ship Victory, in the pay of His M[ajest]ys Navy’ in letters of administration granted by the Admiralty in 1778 to his widow, probably when she was first fitting out), from about 1745 he also worked as a painter, mostly ship portraits, dockyard scenes of shipbuilding and launches, and some other marine views. They combined his knowledge of shipbuilding with accurate architectural and topographical detail. Apparently mostly self-taught, it is possible that dockyard ship-painters also gave him some training in this area. He toured East Anglia, and produced some paintings from notes made on that trip.