The son of George Drew, a tea dealer, of 11 Tottenham Court Road, London, he was born at Louth, Lincolnshire.
Admitted a sizar of St John's College, Cambridge, on 22 January 1839, he took his Bachelor of Arts degree as 27th wrangler in 1843, and was ordained the same year.
He was then vicar of St Barnabas, South Kensington, from 1858 till 1870, was select preacher to the university of Cambridge in 1869–1970, and rector of Avington, Hampshire, during 1870–1873.
Drew, who was a fellow of the Royal Geographical Society, and at one time an active member of the British Association, died suddenly at Holy Trinity vicarage, 21 January 1880.
In 1877 he was elected Hulsean lecturer at Cambridge, and the following year he published his discourses in a volume entitled 'The Human Life of Christ revealing the order of the Universe.... With an Appendix,' London, 1878.