Jackson became, on his recommendation, the sub-preceptor (12 April 1771). From this position he was dismissed in 1776, when all the other persons holding similar places about the princes resigned their posts; but his salary was paid to him for some time afterwards. The Duke of York told Samuel Rogers that Jackson conscientiously did his duty (Recollections of Tabletalk of Rogers, pp. 162–3). John Nicholls attributes his removal to the peevishness of the Earl of Holdernesse, the governor of the prince, and considered it ‘a national calamity’ (Recollections, i. 393–4). Jackson afterwards took holy orders, and from 17 May 1779 to 1783 held the preachership at Lincoln's Inn. In 1779 he was also created canon of Christ Church, Oxford, and in 1783 became dean, whereupon the Prince of Wales wrote a letter of thanks to Fox, expressive of his warm admiration and friendship for Jackson (Memorials of C. J. Fox, ii. 109). Two minor preferments were the rectory of Kirkby in Cleveland, to which he was collated in 1781, and a prebendal stall in Southwell Collegiate Church, which was given to him in 1786.
At Christ Church Jackson soon became famous. He possessed a genius for government, and enforced discipline without any distinction of persons. He took a large share in framing the ‘Public Examination Statute,’ and always impressed upon his undergraduates the duty of competing for exhibitions and prizes. Every day he entertained at dinner some six or eight members of the foundation, and on his annual travel in some part of the United Kingdom took the most promising pupil of the year for his companion. He was a good botanist and a student of architecture, and under his charge the buildings and walks of Christ Church were greatly improved. By some he was considered cold in his manners and arbitrary in his tone, but Polwhele (Traditions, i. 89) and John James, then an undergraduate at Queen's College, praise his kindly bearing (Letters of Radcliffe and James, pp. 146–9). C. Kirkpatrick Sharpe wrote of him in 1798 as ‘a very handsome oldish man’ (Letters of Sharpe, i. 78–9). Copleston highly commended his talent in governing and his love of encouraging youth (Letters of Lord Dudley to Bishop of Llandaff, p. 192). He declined the bishopric of Oxford in 1799 and the primacy of Ireland in 1800. When offered an English see on a later occasion he is said to have remarked: ‘Nolo episcopari. Try Will [i.e. his brother]; he'll take it.’ In 1809 he resigned his deanery, and retired to the Manor House at Felpham, near Bognor, in Sussex. Some Latin lines by himself on this clerical elysium are in the ‘Manchester School Register.’ He died there on 31 Aug. 1819. Over his grave in the churchyard is a stone with his name, age, and date of death only; but the east window of the church, when restored in 1855, was dedicated to his memory. An excellent portrait of him by Owen hangs in Christ Church hall, and has been engraved by C. Turner. From it was executed the statue by Chantrey, which was placed in 1820, at the cost of Jackson's pupils, in the north transept of the cathedral. By the death of his brother without a will considerable wealth fell to him, which was subsequently inherited by his near relation, Cyril George Hutchinson, rector of Batsford in Gloucestershire.
Many illustrious men were under Jackson's charge at Christ Church, among them Canning, Sir Robert Peel, and Charles Wynn. Several letters to and from him are in Parker's ‘Sir R. Peel,’ i. 27–8, and in one of them Jackson characteristically recommends ‘the last high finish’ of oratory by the continual reading of Homer. Abbot, first lord Colchester, was his chief friend, and obtained much political gossip from him. Jackson helped to bring about the removal of Addington from the premiership in 1804. For some years he kept a diary of his life and times, which, with characteristic caution, he afterwards destroyed; but his political intrigues are visible in the ‘Diaries of the first Earl of Malmesbury,’ iv. 255–6, 302, in Lord Colchester's ‘Diary’ (passim), and in Dean Pellew's ‘Life of Lord Sidmouth,’ ii. 302–4. Jackson was considered to excel in Greek scholarship, and about 1802 he and the Rev. John Stokes of Christ Church, Oxford, began printing at the Clarendon press an edition of the history of Herodotus; but it was soon stopped, and almost every copy destroyed. The printed sheets are preserved at the British Museum (cf. Manchester School Register, ii. 272). Parr's not unnatural comment on him was: ‘Stung and tortured as he is with literary vanity, he shrinks with timidity from the eye of criticism.’ Jackson is described under the name of President Herbert in R. Plumer Ward's novel of ‘De Vere,’ and a caricature by Dighton, in which his stoop is well brought out, depicts him as walking with one or two companions.