Burwell was born probably late in the 1730s at Fairfield on Carter’s Creek in Gloucester County, the son of(d. 1756) and Mary Willis Burwell. His father served as president of the and was acting governor of in 1750 and 1751. Little is known about Burwell’s childhood or education, but contrary to what has been written about him, he did not attend Eton, Oxford, or Cambridge or gain admission to the Inns of Court, at each of which his father and some of his other relatives of the same name were educated. Following his father’s death Burwell inherited about 7,000 acres in Gloucester County and other large holdings elsewhere, including approximately 5,000 acres on Bull Run in Prince William County. He inherited and resided at his father’s Fairfield estate, one of the largest and oldest plantation houses in a region of the Tidewater famed even then for its spacious dwellings.
By about 1760 Burwell had married his near neighbor Judith Page, of Rosewell, like him a descendant of Robert “King” Carter and in turn a niece and sister of other councillors. They had two or three sons and two daughters before her death in September 1777. Burwell appears to have been hit hard by the recession early in the 1770s and tried to sell a large tract of land to pay the very “considerable fortunes” that his father’s will had promised to his several sisters. He also had many large claims on his landed wealth, some probably inherited, some perhaps self-acquired. Burwell spent heavily on blooded racehorses, and although he won some handsome purses, he doubtless lost some, too. Whether for that or other reasons, his financial condition appears to have been precarious, as was his physical health.
Burwell was a justice of the peace in Gloucester County beginning in 1765, and in 1767 he was sheriff. From 1769 until 1776 he represented the county in the House of Burgesses. Burwell sat on the Committees for Courts of Justice, of Privileges and Elections, and of Religion, but he never moved into the ranks of the leadership. He took the side of the colonial protestors during the disputes leading up to the American Revolution (1775–1783). Burwell was eligible to serve in all five of the Virginia conventions that met from August 1774 to July 1776 but was absent from the fourth convention and from parts of the third and fifth, probably because of poor health. At the Convention of 1776 he was a member of the Committee of Privileges and Elections. On July 3, 1776, Burwell drew pay for about thirty-two of the fifty-two days of active session. No vote tallies were taken at the convention, but because each major decision passed unanimously, if he was well enough to attend on the day of each pertinent roll call he voted for independence on May 15, for the Virginia Declaration of Rights on June 12, and for adoption of the first written constitution of Virginia on June 29, 1776.
Burwell also represented Gloucester County in the House of Delegates from 1776 to 1778. He served in a low-ranking position on the Committee of Privileges and Elections. Burwell’s death was reported without date and without comment in Dixon and Nicolson’s Williamsburg Virginia Gazette of March 19, 1779. He was buried probably in the family cemetery at Fairfield. Within weeks Burwell’s fine stable of horses and his valuable household furniture went on the auction block. His death brought to an end a full century of Burwell family residence and political distinction at Carter’s Creek in Gloucester County.