Career
In 1632 he was admitted at Magdalen Hall, Oxford. He entered Middle Temple in 1634 and was called to the bar in 1641. He was Justice of the Peace for Sussex from 1647 to 1649 and from 1654 was Recorder of Chichester from 1654.
He became Justice of the Peace for Sussex again in 1655 and held the position until his death.
In 1656 he was re-elected Member of Parliament for Chichester in the Second Protectorate Parliament. He was commissioner for assessment for Sussex in 1657 and became Recorder of Portsmouth in 1658 until his death.
In 1659, he was re-elected Member of Parliament for Chichester in the Third Protectorate Parliament. He became commissioner for assessment for Sussex from January 1660 until his death.
In March 1660 he became commissioner for militia for Sussex and in April 1660 he was re-elected Member of Parliament for Chichester in the Convention Parliament.
He was commissioner for oyer and terminer on the Home circuit in July 1660 and commissioner for sewers in West Sussex in October 1660. In 1661 Peckham was re-elected Member of Parliament for Chichester in the Cavalier Parliament. He became Recorder of Newport Isle of Wight after 1661 and was knighted on 24 May 1662.
He became bencher of his Inn in 1663 and was commissioner for assessment for Chichester from 1663 to 1664.
In 1669 he became serjeant-at-law and was reader of his inn. Peckham died at the age of 57 and was buried at the church of Street Peter the Great, Chichester on 27 April 1673.
Her elder brother was Sir Henry Goring, 2nd Baronet. They had eight children but only the third son John produced a Peckham grandson, who was the childless Henry « Lisbon » Peckham (1683-1764), owner of Pallant House.
Their second son Henry was mayor of Chichester in 1681 and 1686.