His degrees were B.A. 1738–9, M.A. 1742, B.D. 1749, and D.D. 1757; and on 25 March 1740 he was admitted as fellow of St. John's.
In 1741 Powell became private tutor to Charles Townshend (second son of Viscount Townshend), afterwards chancellor of the exchequer. At the end of that year he was ordained deacon and priest, and was presented on 13 Jan. 1741–2 by Lord Townshend to the rectory of Colkirk in Norfolk. In 1742 he returned to college life, and, after reading lectures for two years as assistant tutor, was promoted in 1744 to be principal tutor, and acted in 1745 as senior taxor of the university. While he was at Cambridge his chief friends were Balguy and Hurd. Mason, who was then an undergraduate at St. John's, refers in a contemporary poem to ‘gentle Powell's placid mien.’ On 3 Nov. 1760 he became a senior fellow of his college, and in 1761, when he had inherited the property of his cousin, he quitted Cambridge and took a house in London; but he did not resign his fellowship until 1763.
While at Cambridge Powell twice provoked a serious controversy. There was printed in 1757, and reprinted in 1758, 1759, and 1772, a sermon, entitled ‘A Defence of the Subscriptions required in the Church of England,’ which he had preached before the university on Commencement Sunday. He contended that the articles were general and indeterminate, and ‘left room for improvements in theology.’ These views were much criticised by partisans on both sides, Powell's chief avowed opponent being Archdeacon Blackburne, who published severe ‘Remarks’ upon the sermon in 1758 (cf. Meadley, Life of Mrs. Jebb, p. 59).
Powell's second controversy was of a personal character. The Lucasian professorship was vacant in 1760, and among the candidates were Edward Waring of Magdalene College and William Ludlam of St. John's College. As some evidence of his qualifications for the post, Waring distributed a portion of his ‘Miscellanea Analytica,’ and to serve the interests of Ludlam, a member of his own body, Powell attacked it in ‘Observations on the First Chapter of a Book called “Miscellanea Analytica”’ (anon.), 1760. To a reply by Waring, Powell retorted in an anonymous ‘Defence of the Observations,’ which Waring answered in a ‘Letter.’
On 25 Jan. 1765 Powell was unanimously elected master of his old foundation of St. John's College, Cambridge, where he spent the rest of his days ‘in great splendour and magnificence.’ There were numerous competitors for the post, but he was backed by the influence of the Duke of Newcastle (Gray, Works, ed. Gosse, iii. 190). Hurd congratulated him on owing the election to his own merit (Kilvert, Life of Hurd, p. 93). Powell had been admitted a fellow of the Royal Society on 15 March in the previous year. In the following November he succeeded to the vice-chancellorship of the university, and in December 1766 he was appointed by the crown to the archdeaconry of Colchester. In 1768 he claimed the college rectory of Freshwater in the Isle of Wight, worth 500l. per annum, which was in the option of the master, and resigned the benefice of Colkirk. The fellows disliked this act, but their indignation was somewhat mitigated by Powell's gift of 500l. to the society, when it was intended to rebuild the first court and to lay out the gardens under the care of ‘Capability’ Brown. Through the watchfulness with which he guarded the corporate revenues and the strictness of his discipline the college secured the leading position in the university. In its first year he established college examinations, drawing up the papers himself (cf. Wordsworth, Scholæ Academicæ, pp. 354–6), and attending the examinations in person. But he opposed with vigour the proposition of Dr. Jebb that annual examinations of the whole university for all students in general subjects should be established. An anonymous pamphlet, ‘An Observation on the Design of establishing Annual Examinations at Cambridge,’ 1774, is ascribed to him, and it provoked from Mrs. Jebb ‘A Letter to the Author.’ He helped several undergraduates with the means of completing their course, and, at his own expense, he bestowed prizes; but he did not allow any student, whatever his year might be, to pass without examination in one of the gospels or the Acts of the Apostles. He himself attended chapel without a break through the whole year, at six o'clock in the morning. His manners, however, were ‘rigid and unbending.’
About 1770 Powell had a stroke of apoplexy, and he died in his chair, from a fit of the palsy, on 19 Jan. 1775. He was buried in the college chapel on 25 Jan., the anniversary of his election as master, and over his vault was placed a flat blue stone, with an epitaph by Balguy. He was unmarried, and left his property to his niece, Miss Jolland, who lived with him. For his sister, Susanna Powell, with whom he could not agree, an annuity of 150l. was provided. She became matron of the Chelsea Hospital, and died at Colchester in August 1796. He bequeathed 1,000l. to Dr. Balguy, and the same sum for equal division between six fellows and four members of his college. His books were left to four of the fellows.