A native of Cornwall, England, he was nicknamed the "Cornish metaphysician" for his works on the human soul, the nature of God, and the deity of Christ.
In 1798 the first part of Thomas Paine's Age of Reason was put into his hands; and in the following year he made his first appearance as an author by publishing his Remarks on that work.
Drew had begun to meditate a greater attempt before he wrote his Remarks on Paine; and, encouraged by the antiquary John Whitaker, he published his Essay on the Immateriality and Immortality of the Soul in 1802.
This work made the "Cornish metaphysician," as he was called, widely known, and for some time it held a high place in the judgment of the religious world as a conclusive argument on its subject.
Drew continued to work at his trade until 1805, when he entered into an engagement with Dr Thomas Coke, a prominent Wesleyan official, which enabled him to devote himself entirely to literature.
In 1819 he removed to Liverpool, being appointed editor of the Imperial Magazine, then newly established, and in 1821 to London, the business being then transferred to the capital.
The work which he then wrote, and which in his own judgment was his best, was published in 1820, under the title of An Attempt to demonstrate from Reason and Revelation the Necessary Existence, Essential Perfections, and Superintending Providence of an Eternal Being, who is the Creator, the Supporter, and the Governor of all Things (2 vols 8vo).