He received his musical training from his father, Charles Babel, a bassoonist in the Drury Lane orchestra, Johann Christoph Pepusch and possibly George Frideric Handel.
From November 1718 until his death, he was organist at All Hallows, Bread Street, and was succeeded by John Stanley.
These were published in France, the Netherlands and Germany as well as in England, and formed the basis of his musical reputation.
Johann Mattheson thought he surpassed Handel as an organ virtuoso, but music historian Charles Burney criticised his manner of playing arrangements, charging that he: acquired great celebrity by wire-drawing the favourite songs of the opera of Rinaldo, and others of the same period, into showy and brilliant lessons, which by mere rapidity of finger in playing single sounds, without the assistance of taste, expression, harmony or modulation, enabled the performer to astonish ignorance, and acquire the reputation of a great player at a small expence … Mr Babel … at once gratifies idleness and vanity.Despite Burney's criticism, fellow music historian Sir John Hawkins thought they 'succeeded so well ... as to make from it a book of lessons which few could play but himself, and which has long been deservedly celebrated.'
Babell also wrote original sonatas for violin or oboe and continuo, concertos and other miscellaneous works, including an Ode for St. Cecelia's day, now lost.