A son of William Dowdeswell of Pull Court, Bushley, Worcestershire, he was educated at Westminster School, at Christ Church College, Oxford, then at the University of Leiden. He became member of parliament for the family borough of Tewkesbury in 1747, retaining this seat until 1754, and from 1761 until his death he was one of the representatives of Worcestershire. Becoming prominent among the Whigs, Dowdeswell was made Chancellor of the Exchequer in 1765 under the Marquess of Rockingham, and his short tenure of this position appears to have been a successful one, he being in Lecky's words a good financier, but nothing more.
To general astonishment, he refused to abandon his friends and to take office under Chatham, who succeeded Rockingham in August 1766. Dowdeswell then led the Rockingham party in the House of Commons, taking an active part in debate until his death at Nice. The highly eulogistic epitaph on his monument at Bushley was written by Edmund Burke.