He was third son of John Senhouse (d. 1604) of Netherhall, Cumberland (now part of Maryport), by Anne, daughter of John Ponsonby of Hail Hall and the great-great-nephew of William Senhouse, bishop of Carlisle and Durham.
[1] His father was an antiquary who collected Roman remains, and Sir Robert Bruce Cotton visited him in 1599.
[3] He was known as a preacher, and became chaplain successively to Edward Russell, 3rd Earl of Bedford, Prince Charles, and King James I.
In 1606 he was appointed vicar of Bumpsted Steeple, Essex; in 1608 he was rector of Cheam, Surrey, and on 18 December 1621 he became dean of Gloucester.
He was made bishop of Carlisle on 26 September 1624, and preached the coronation sermon for Charles I on 2 February 1626.