Jenner was a citizen and goldsmith of the City of London. By 1627 he acquired the manor of Widhill in WIltshire. He also acquired the manor of Eysey.
In April 1640, he was re-elected Member of Parliament for Cricklade in the Short Parliament.
He was re-elected Member of Parliament for Cricklade in November 1640 for the Long Parliament, and held the seat until he was excluded under Pride"s Purge in 1648. Jenner was in favour of taking a milder course with Charles I at the end of the Civil War, and was reprimanded by Oliver Cromwell for his tenderness.
In 1648 he acquired the manor of Marston Meysey. Jenner died at the age of 67 and was buried in Cricklade Street Sampson’s Church.
He left money for eight almshouses in Malmesbury and for the building and maintenance of a free school at Cricklade.
In 1652 a school was built backing onto Street Sampson"s Churchyard. Later the building became the parish workhouse before going back into use as a school until 1959. lieutenant became the Cricklade parish hall and was renamed the Jenner Hall.
Jenner married Elizabeth Longston, daughter of Thomas Longston, citizen and grocer of London.