Poulett was the son of Sir Anthony Poulett (1562–1600) (also spelt Paulet), of Hinton St George, Governor of Jersey, and Captain of the Guard to Queen Elizabeth by his wife Catherine Norris, daughter of Henry Norris, 1st Baron Norreys (1525–1601) of Rycote in Oxfordshire.
He was educated at University College, Oxford and was admitted as a student of the Middle Temple in 1610.
He served in the Royal Navy to secure English commerce and bullion ships from Dutch raiding expeditions.
At the start of the Civil War he put his signature, together with those of other Lords and Councillors, to a declaration disavowing any intention by King Charles I to wage war against the Parliament, but as hostilities broke out he sided, on 15 June 1642, with the Royalist cause.
At war's end, Parliament gave him a pardon, but his house was constrained to settle a large sum in reparations.