Whitmore was the son of Thomas Whitmore of Apley Park near Bridgnorth and his wife Catherine Thomasson, daughter of Thomas Thomasson of York. His father was Member of Parliament (MP) for Bridgnorth from 1806 to 1831. Whitmore was educated at Christ Church, Oxford. He was a Deputy Lieutenant and J.P. for Shropshire.  He served as cornet in the South Salopian Yeomanry Cavalry in 1845.
At the 1852 general election, Whitmore was elected MP for Bridgnorth in succession to his brother Thomas Charlton Whitmore. A petition was lodged against his election, but it was dismissed. He was Lord of the Treasury and keeper of the Privy Seal to the Prince of Wales from March 1858 to June 1859. In 1865 he lost the seat in the election but his opponent's election was overturned and he was reinstated after petition. He was a Lord of the Treasury from July 1866 to December 1868. In 1868, representation for Bridgnorth was reduced to one member, but Whitmore was returned and held the seat until 1870. He was party whip for many years until 1869.
Whitmore married Adelaide Anna Darby, daughter of Francis Darby of Coalbrookdale, in 1852. He died at the age of 62.
- Debretts House of Commons and the Judicial Bench 1870
- Gladstone, E.W. (1953). The Shropshire Yeomanry 1795-1945, The Story of a Volunteer Cavalry Regiment. The Whitethorn Press. p. 45.
- Leigh Rayment's Historical List of MPs – Constituencies beginning with "B" (part 5)[self-published source][better source needed]
- Hansard 1803–2005: contributions in Parliament by Henry Whitmore
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