Educated at Winchester and at Wadham College, Oxford, he became a barrister and in 1720 entered parliament as a member for the borough of Guildford. Seven years later he became one of the members for Surrey, and he retained this seat until 1761. In 1728 he was elected Speaker of the House of Commons, being the third member of his family to hold this office; he was also chancellor to George II's queen, Caroline, and from 1734 to 1742 he was treasurer of the navy.
He retired from the position of Speaker and from parliament in 1761, and enjoyed an annuity of £3000 until his death. As Speaker, Onslow was a conspicuous success, displaying knowledge, tact and firmness in his office; in his leisure hours he was a collector of books.
Speaker Onslow's nephew, George Onslow (1731-1792), a son of his brother Richard, was a lieutenant-colonel and member of parliament for Guildford from 1760 to 1784. He had a younger brother Richard (1741-1817), who entered the navy and was made an admiral in 1799.