See biographies by N. Gash (2 vol., 1961-72) and D. Read (1987).
He was the son of Sir Hugh Inglis, a minor politician and MP for Ashburton (1802-1806). Robert, who succeeded to his father's baronetcy in 1820, was MP for Dundalk 1824-1826, Ripon 1828-1829 and Oxford University from 1829 to 1854.
Inglis was strongly opposed to measures which, in his view, weakened the Anglican Church. When Robert Grant, MP for Inverness Burghs (UK Parliament constituency), petitioned for Jewish relief in 1830, Inglis was violently opposed. Inglis alleged that the Jews were an alien people, with no allegiance to England, and that to admit Jews to parliament would "separate Christianity itself from the State." He also alleged that if they were admitted to parliament "within seven years...Parliamentary Reform would be carried." Inglis was joined in his public opposition by the Chancellor of the Exchequer, Henry Goulburn, and the Solicitor General and future Lord Chancellor, Sir Edward Sugden. Although the Jews were not emancipated fully until 1858, Parliamentary Reform occurred in 1832, just two years later. Inglis also likened Buddhism to "idolatry" in connection with the British colony of Ceylon during a debate over the relationship of "Buddhist priests" to the British colonial government in 1852.
In 1845 he broke with Sir Robert Peel and opposed the Maynooth Grant, which would have granted a yearly £26,000 subsidy to the Catholic Maynooth seminary. Other opponents included, oddly enough, John Bright and Benjamin Disraeli, although on different grounds.
In 1851, when Lord Stanley (who became the Earl of Derby later that year) attempted to form a protectionist administration, Inglis was offered the presidency of the Board of Control, which he accepted initially, only to withdraw a few days later. A major activity of Inglis's political career was the chairing of the select committee that controlled the House of Commons Library, of which he was a member for 14 years. However, his rather narrow view of its scope was overturned by Sir Robert Peel in 1850. He was made a Privy Counsellor in 1854, and died the next year, at the age of 69. On his death the baronetcy became extinct.
Inglis's Journals are in the Canterbury cathedral Library and archives.