[2] Vane was Member of Parliament (MP) for the City of Durham from 1794 to 1800, replacing his uncle John Tempest, Jr., who died in a riding accident in 1793.

[3] He accepted the Chiltern Hundreds in 1800 before returning to Parliament as representative for the County Durham from 1807 until his death from apoplexy in 1813.

In a match with Mr. Cookson's Diamond over the Beacon Course at Newmarket in 1799, Hambletonian won by a neck, Sir Henry having wagered 3,000 guineas on the outcome.

The aftermath is the subject of George Stubbs' painting "Hambletonian Rubbing Down", which is preserved at Mount Stewart.

[7] On 25 April 1799 by special licence, Vane-Tempest married Anne MacDonnell, 2nd Countess of Antrim at her mother's house in Hanover Square.

This provision was complied with when Frances Anne married Lord Charles William Stewart in 1819.