Bennet was the second of three sons and fourth of eight children of Charles Bennet, 4th Earl of Tankerville, and his wife, Emma (1752–1836), daughter of banker Sir James Colebrooke, 1st Baronet.
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At the request of William Wilberforce and Henry Grey Bennet (who was then Shrewsbury's local Member of Parliament) in 1808 he drew up a report on the management of factories, as an answer to a claim made in parliament that manufactories were hotbeds of vice.