Born in Plymouth Dock, Devonshire in 1746.
He followed his father to work for John Smeaton, the engineer responsible for rebuilding the Eddystone Rock lighthouse. Jessop served Smeaton as apprentice from 1759 to 1767 and as his assistant until 1772.
After Smeaton’s retirement, Jessop became the outstanding man in his profession and undertook canal, harbour works and land drainage projects in England, Scotland and Ireland. He was founder of the Butterley Iron Works in Derbyshire and promoted the use of cast iron as a constructional material in viaducts and railways.
He designed harbour improvement projects such as the West India docks in London. In Bristol his plan to divert the River Avon along the 1.8 miles of the New Cut was carried out between 1804 and 1809. This allowed 80 acres of tidal river to be enclosed to form the Floating Harbour.
Jessop lived and worked in Newark where he served twice as Mayor. He had 7 sons, 4 of whom also became engineers, and 1 daughter.
At the time of his death in 1814 the family home was Butterley Hall, Derbyshire.