David passed through the Kibworth grammar school, and studied for the ministry (1709–14) at the Fund Academy in Moorfields, under Isaac Chauncy and his successors, Thomas Ridgley, D.D., and John Eames.
In March 1715 he was chosen evening lecturer at Rotherhithe; in June 1716 he became assistant to John Foxon at Girdlers' Hall, Basinghall Street; on 19 May 1718 he was called to succeed Thomas Simmons as pastor of the independent congregation, Wapping New Stairs.
Jennings's career as a divinity tutor began in 1744, on the death of Eames, whose successor he became under the Coward trust, the "congregational" fund at this point transferring its support to another academy.
Two of his students, Thomas and John Wright, afterwards presbyterian ministers in Bristol, were expelled on grounds of doctrine; in fact the majority of his pupils became Arians, according to Alexander Gordon writing in the Dictionary of National Biography.
His eldest son, Joseph, married a daughter of Daniel Neal, by Elizabeth, sister of Nathaniel Lardner.