He was third son of eleven children of Charles David Brereton (1790–1868), for forty-seven years rector of Little Massingham and his wife Frances (1796–1880), daughter of Joseph Wilson of Highbury Hill, Middlesex, and Stowlangtoft Hall, Suffolk.
Brereton was educated at Islington proprietary school under John Jackson, afterwards bishop of London, and at Rugby under Thomas Arnold (1838–41).
He gained a scholarship at University College, Oxford, in 1842, obtained the Newdigate Prize for a poem on the Battle of the Nile in 1844, and graduated B.A.
The journal promoted and reported on the grand celebration held on 25 October 1849 at Wantage of the millennium of the birth of Alfred the Great.
Brereton's interest in educational reform among the agricultural and middle classes was stimulated by his father's studies of the Poor Laws and also by the influence of Thomas Arnold at Rugby School.
Having been appointed rector of West Buckland in North Devon, with the encouragement and practical assistance of Hugh Fortescue, 2nd Earl Fortescue (d.1861), KG, lord-lieutenant of Devonshire, and his son Viscount Ebrington (d.1905), Brereton established in 1858 at West Buckland the farm and county school to supply education suitable for farmers' sons.
Indeed, although religious instruction and worship were part of the curriculum at Brereton's schools the low church approach was less discouraging to non-conformist elements of the middle classes.
Finally, Brereton did not rely wholly on endowments as did Woodard, but he operated mainly on a proprietary basis, forming companies of investors to raise the capital needed to found his schools.
Brereton's removal to Little Massingham in 1867 as rector led in 1871 to the foundation there of the Norfolk County School, which was transferred in 1874 to North Elmham.
The undergraduates were younger than was customary, and the cost of board and tuition, which was covered by an inclusive charge of eighty guineas a year, was much lower than in the established colleges.
Similar efforts in west Norfolk led to the Lynn and Fakenham Railway, which was subsequently extended to Norwich, Cromer, and Yarmouth.