His son, Joseph Pett of Limehouse, succeeded his father as Master Shipwright before Peter's death in 1605.
Joseph surveyed the timber for the construction of a ship named Sovereign of the Seas, and married Elizabeth, daughter of Richard Hoborn, another shipwright and churchwarden at Chatham.
Joseph's son, the second Peter Pett, carried on the private family business of shipbuilding at Wapping.
Phineas Pett succeeded shipwright John Holding in the post of keeper of the plank yard, but his income was meagre by the standards set by his family.
In his diary, he recorded that it became his duty, for which he considered himself unfit, to take charge of the affairs of his "poor sisters and brother."
Phineas' son Peter, commissioner of Chatham, was disgraced because of the Battle of Medway and the loss of capital ships almost 100 years later.