He is particularly noted for commissioning the design and construction of Holkham Hall in north Norfolk. He was honoured by being created first Earl of Leicester, in a recreation of an ancient earldom. As a young man, Coke embarked on a six-year "Grand Tour", returning to England in the spring of 1718.
Both were later to be engaged by Coke to work on his mansion at Holkham which housed the considerable collection of works of art that Coke had accumulated on his travels.
In 1717, during these travels he purchased the Codex Leicester, containing some of the works of Leonardo da Vinci, the Italian artist and scientist However, Coke was badly affected by financial losses when his investments in the South Sea Company proved worthless.
This delayed the building of Coke"s planned new country estate for over ten years. lieutenant was not until around 1732 that Burlington and Kent made their first drawings for the new country house.
Norfolk architect Matthew Brettingham was also influential in the design of the mansion (though he attributed the design of the Marble Hall to Coke himself).
Work on the foundations began in 1734, but it was to be 30 years before work was completed. I look around not a house to be seen but my own. I am Giant of Giant Castle and have ate up all my neighbours my nearest neighbour is the King of Denmark.”
Coke, who had been created Earl of Leicester in 1744, died in 1759, five years before the completion of Holkham, having never fully recovered his financial losses.
Between 1722 and 1728, he was one of the two Members of Parliament for Norfolk.