He was born on 20 May 1760 at Gilling in the North Riding of Yorkshire; his father Matthew Raine was vicar of St. John's, Stanwick and rector of Kirkby Wiske, and also master of a school at Hartforth, while his mother Esther was from Cumberland.
In 1783 and 1784 he gained the members' university prize, and in the latter year was also made Fellow of Trinity.
[1] After some time spent in tutoring, Raine was appointed headmaster of Charterhouse School on 7 June 1791, in succession to Samuel Berdmore: Charles Burney was one of his competitors.
He was buried in the chapel of the Charterhouse, where there was a gravestone in the south aisle inscribed M. R., and a mural tablet on the adjoining wall by John Flaxman, with an epitaph by Samuel Parr—Parr and Richard Porson were close friends.
His collection of classical books, including rare editions, went by bequest, after the death of his brother Jonathan Raine, to the library of Trinity College, Cambridge.