Born in Southwark, Cleveley was an apprentice joiner and later went on to work in the Royal Dockyard at Deptford where he settled. One explanation for where, or from whom, Cleveley learnt his considerable skill as a painter is that following the scandal of the cost of the carved decorations on the Royal Sovereign of 1701, the Admiralty decreed in 1704 that only the head and stern galleries of ships could have carved decorations, while the rest must be in paint. Thus many woodcarvers were paid off in the Royal dockyards and decorative painters taken on to paint the trophies of arms, classical figures, chariots, and so on, which adorned the sides of most ships from head to stern at the level of the upper-deck gunwales and above.

John Cleveley could have learnt to paint from one or some of these dockyard painters and by his own genius refined his work to easel painting. He painted a series a launches of ships at Deptford and also painted ship portraits, a few battle pieces, and Royal occasions.