Herbert was the sixth and youngest son of Henry Herbert, 1st Earl of Carnarvon by Elizabeth Alicia Maria, elder daughter of Charles Wyndham, 2nd Earl of Egremont. He was educated at Eton from 1805 onwards, and progressed to Christ Church, Oxford, where he matriculated on 23 October 1810. He went on to study at Exeter College, and graduated B.A. in 1813 and M.A. in 1825. He was elected a fellow of Merton College in 1814; became sub-warden in 1826, and dean in 1828.
On 27 November 1818 he was called to the bar at the Inner Temple. Herbert was the author of some remarkable works replete with abstruse learning. They are, however, discursive, and his arguments are inconclusive.
He married, on 2 August 1830, Marianne, sixth daughter of Thomas Lempriere of La Motte, Jersey; she died on 7 August 1870. They had one son, Sir Robert George Wyndham Herbert, and two daughters. Herbert died at Ickleton, Cambridgeshire.
His works were:
- Nimrod, a Discourse upon Certain Passages of History and Fable, 1826; reprinted and remodelled in 2 vols., 1828, with a third volume in the same year, and vol. iv in 1829–30.
- An article on "Werewolves", by A. Herbert, pp. 1–45, in The Ancient English Romance of William and the Werwolf (ed. F. Madden, Roxburghe Club, 1832).
- Britannia after the Romans, 1836–41, 2 vols.
- Nennius, the Irish version of the Historia Britonum. Introduction and Notes by A. Herbert, 1848.
- Cyclops Christianus, or the supposed Antiquity of Stonehenge, 1849.
- "On the Poems of the Poor of Lyons", and three other articles in the appendix to J. H. Todd's Books of the Vaudois (1865), pp. 93, 126, 135, 172.
- Boase, George C. (1891). "Herbert, Algernon (1792–1855), antiquary". Dictionary of National Biography Vol. XXV. Smith, Elder & Co. Retrieved 2007-11-20.