His mother was Frances Harriet, daughter of Rear-Admiral of the Red John Barker, R.N.
Charles Jenkinson, 1st Earl of Liverpool, was his uncle, and Robert Jenkinson, 2nd Earl of Liverpool, Prime Minister of the United Kingdom in 1812–1827, was his first cousin.
Jenkinson was returned to Parliament as one of two representatives for Dover in 1806, a seat he held until 1818.
In 1851, at the age of 72, he succeeded his cousin Charles Jenkinson, 3rd Earl of Liverpool, as tenth Baronet, of Walcot and Hawkesbury.
Jenkinson died without male issue in March 1855, aged 76.