Heytesbury was the eldest son of Sir William à Court, 1st Baronet, and Laetitia, daughter of Henry Wyndham.

He was also Envoy Extraordinary to the Barbary States from 1813 to 1814, to the Kingdom of Naples in 1814 and to Spain from 1822 to 1824 and served as Ambassador to Portugal between 1824 and 1828.

The latter year Heytesbury was appointed Ambassador to Russia, where he had to deal with the Russo-Turkish War of 1828 to 1829 and the tensions created by the Russian Empire's occupation of the Danubian Principalities.

In 1835 Sir Robert Peel nominated him for the office of Governor-General of India, but the Tory government soon fell and he never took up the post.

Heytesbury succeeded his father as second Baronet in 1817, was admitted to the Privy Council the same year and made a GCB in 1819.