He failed to inherit the hereditary baronetcy, as he died in 1794, before his father's death in 1797.

His mother Elizabeth died when he was young on 24 August 1747 and his father married again.

When Burdett came of age his father was having the ancestral home of Foremarke Hall remodelled.

Burdett was the brother-in-law of Francis Mundy and a member of the private Markeaton Hunt.

Each of the subjects was in the distinctive dress of the Markeaton Hunt, consisting of a blue coat over a scarlet waistcoat and yellow breeches.