After attending the high school of Edinburgh and the university of Glasgow, he entered Balliol College, Oxford, where he graduated B.A. in 1834 and M.A. in 1836. He was admitted a member of the Faculty of Advocates, Edinburgh, in 1835, and soon acquired a reputation as an eloquent and skilful pleader. As an advocate his most famous achievement was his brilliant defence in 1857 of Madeline Smith, accused of poisoning. The jury returned a verdict of not proven.
In politics Inglis was a conservative, and on the accession of Lord Derby to power in February 1852 he was made solicitor-general of Scotland, this office being, after the general election three months later, exchanged for that of lord advocate. He resigned his post on the defeat of Lord Derby's government in November, and was elected immediately afterwards dean of the Faculty of Advocates. On the return of Lord Derby to power in 1858, he again became lord advocate, and on 3 March was returned to the House of Commons as member for Stamford, but his political career was brought to a close on 13 July of the same year, when he was raised to the bench as lord justice-clerk and president of the second division of the court of session. The only important piece of legislation associated with his name is the Universities of Scotland Act of 1858. Though founded on a bill drafted by his predecessor in office, it was rendered, by the introduction of material modifications, practically a new measure. It met with general approbation, and his services both in preparing it and guiding it through the House of Commons were acknowledged by his election to the permanent chairmanship of the commission appointed by the act, and the conferment on him in December 1858 of the degree of doctor of laws by the university of Edinburgh. In 1859 he was also created a D.C.L. by the university of Oxford. In the same year he was sworn a member of the privy council.
On the death of Lord Colonsay [see MacNeill, Duncan], Inglis was on 26 Feb. 1867 installed lord justice-general of Scotland, and lord president of the court of session, taking the title of Lord Glencorse. Except Lord Stair, no Scottish judge has ranked so high as a jurist. As an exponent of law he owed much to his severe conscientiousness and impartiality, and to his reverence for Scottish jurisprudence as an independent national system. But his chief strength as a judge lay rather in a ‘certain beneficent sagacity, a luminousness of mind, a humanity of intelligence, which might almost be regarded as unique’ (Scots Observer, 19 July 1890). He was uniformly patient, courteous, and dignified.
Outside his judicial duties Inglis did much useful work. He was an active member of the board of manufactures, and, besides rendering important services to higher education in Scotland as permanent chairman of the university commission appointed in 1858, he was a governor of Fettes College, Edinburgh; was in 1857 chosen lord rector of King's College, Aberdeen, and in 1865 of the university of Glasgow; and as chancellor of the university of Edinburgh, to which, in opposition to Mr. Gladstone, he was elected in 1869, took a practical share in the administration of university affairs. His inaugural addresses at Aberdeen, Glasgow, and Edinburgh (1869) were published separately. He was president of the Scottish Text Society, and of his antiquarian tastes he gave incidental evidence in 1877 in a privately printed paper on the name of his parish, Glencorse, which was identical with the name of his own estate. The paper was written in protest against a proposal officially to change the name to Glencross. A valuable and succinct paper on ‘Montrose and the Covenanters of 1638,’ was published in ‘Blackwood's Magazine’ for November 1887. Its chief aim is to vindicate the character of Montrose. Inglis's ‘Historical Study of Law, an Address to the Juridical Society,’ appeared at Edinburgh in 1863.
Inglis was a keen golfer, and was once elected to the annual honorary captaincy of the golf club of St. Andrews. On his estate of Glencorse he took a special interest in the cultivation of trees. Though latterly somewhat broken in bodily health, he continued in office to the close of his life. He died, after a few days of prostration, at his residence of Loganbank, Midlothian, on 20 Aug. 1891, just before completing his eighty-first year. By his wife Isabella Mary, daughter of the Hon. Lord Wood, a judge of the court of session, he left two sons, A. W. Inglis, secretary to the board of manufactures, and H. Herbert Inglis, writer to the signet.
The original portraits of Inglis are a chalk drawing by John Faed, R.S.A., in possession of A. W. Inglis, esq., engraved by Francis Holl, about 1852; a full-length portrait by Sir John Watson Gordon, P.R.S.A., 1854, now in the university of Edinburgh; a Kit-Cat portrait in his justiciary robes as lord justice-clerk, by Sir Francis Grant, P.R.A., in possession of A. W. Inglis, esq.; bust in marble by William Brodie, R.S.A., engraved privately for James Hay, esq., Leith, now in the hall of the Parliament House, Edinburgh; portrait, in a group representing a family shooting-party, by Gourlay Steell, R.S.A., 1867, in possession of A. W. Inglis,