Brekell was born at North Meols, Lancashire, in 1697, and was educated for the ministry at Nottingham, at the dissenting academy of John Hardy.
His ministry covers the period between the rise of the evangelical liberalism of Philip Doddridge (his correspondent, and the patron of his first publication), and the avowal of Socinianism by Joseph Priestley, to whose Theological Repository he contributed in the last year of his life.
His first publication was The Christian Warfare … a Discourse on making our Calling and Election sure; with an Appendix concerning the Persons proper to be admitted to the Lord's Supper, 1742.
Following the example of his predecessor, he preached and published a sermon to sailors, Euroclydon, or the Dangers of the Sea considered and improved, &c. (Acts xxvii.
The Divine Oracles, or the Sufficiency of the Holy Scriptures, &c., 1749, is a reply to a work by Thomas Deacon, M.D., of Manchester, a nonjuring bishop.
Brekell's name appears among the subscribers to a work by Whitfield, a Liverpool printer and sugar refiner, who had left the presbyterians, entitled A Dissertation on Hebrew Vowel-points.
He published a dissertation on Circumcision, 1763, a volume of sermons, The Grounds and Principles of the Christian Revelation, 1765, and A Discourse on Music, 1766.
36) dedicated 'more especially to the Gentlemen Volunteers of Liverpool, and the Regiment of Blues raised at their own expense by that Loyal Town and Corporation.
At the end is a warlike 'Hymn suitable to the Occasion of the general Fast to be observed with a view to the present War, both Foreign and Domestic'); also a Sermon (Phil.