He was born in Slingsby, Yorkshire the second son of Thomas, a London Attorney of the Inner Temple, and Elizabeth (nėe Berriman) Baber and was educated at St Paul's School, London. He entered All Souls College, Oxford and graduated MA in 1805.
After working for a while as a sub-librarian at the Bodleian Library, Oxford he became in 1807 Assistant Librarian at the British Museum. In 1812 he was promoted to Keeper of the Printed Books. The crown rewarded him with the rectory of St James' Church, Stretham, Cambridgeshire in 1827, for his work on a three-volume edition of the Old Testament part of the Codex Alexandrinus. He was elected in May 1816 a Fellow of the Royal Society 
When the museum trustees decided in 1837 that their staff should no longer hold other remunerated posts, Baber resigned from his museum post but remained rector of Stretham until his death aged 94. He had married in 1809 Ann Smith, the daughter of Harry Smith. They had two sons and three daughters.
His published works include:
- Librorum Impressorum Qui in Museo Britannico Adservantur Catalogus ... (Latin Edition) - Paperback (26 February 2010) by Henry Ellis, Henry Hervey Baber
- The New Testament: Translated From The Latin In The Year 1380 By John Wiclif (1810) - Hardcover (23 May 2010) by John Wycliffe and Henry Hervey Baber
- "Baber, Henry Hervey". Dictionary of National Biography. London: Smith, Elder & Co. 1885–1900.
- "HENRY HERVEY BABER, ( 1775-1869)". Retrieved 5 December 2010.
- Persons: Baber, Henry Hervey (1827–1827) in "CCEd, the Clergy of the Church of England database" (Accessed online, 2 February 2014)
- "Library and Archive Catalogue". Royal Society. Retrieved 5 December 2010.
- Oxford Dictionary of National Biography (ODNB):Henry Hervey Baber (online ed.). Oxford University Press. 2004–2010. (subscription required)
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