Burchett served on Russell's flagship, the 100-gun HMS Britannia, at the battle of Barfleur in 1692 during the War of the Grand Alliance. In 1693 he became the Deputy Judge Advocate of the Fleet, replacing Samuel Pepys in that office. Burchett was elected as a member of the English Parliament in 1705 as a Whig and member of the 'Court Group' representing the borough of Sandwich, in Kent. He remained a Member of Parliament (MP) until 1713, then returned in 1721 continuing as a member for 20 years.