The son of another John Burrell, whom he eventually succeeded as Rector of Letheringsett, Norfolk, and the grandson of John Holmes, for thirty years Master of Holt School, Burrell was baptised at Letheringsett on 20 September 1762.
He was educated by James Smith at Holt School before being admitted to the lists of Sidney Sussex College, Cambridge, on 6 July 1779.
On 22 May 1785 he was ordained a deacon at Norwich and a few months later, on 18 December, became a priest of the Church of England.
In 1786 he succeeded his father as Rector and patron of Letheringsett, a benefice he held until his death.
[1] Burrell published a Prodromus lepidopterorum Britannicorum and several papers on the moths, beetles, and true bugs of Norfolk.