He was the eldest son of William Cook, whose father had acquired Broome Hall by marriage in 1603. The 1st Baronet remained neutral in the English Civil War, though he did sign the Norfolk address to George Monck for a free parliament in 1660 and was made a baronet three years later. The 2nd Baronet's mother was the 1st Baronet's first wife, Mary Astley, daughter of Thomas Astley of Melton Constable. He attended Emmanuel College, Cambridge from 1647 and Gray's Inn from 1648 and was noted as "very well versed in every kind of learning, but especially distinguished by the suavity of his manners". He was a Justice of the Peace for Norfolk from 1660 to 1668 and a captain in the militia from around October 1660 to 1679 or possibly later. He became a commissioner for assessment Norfolk in 1661 and for Suffolk in 1679, holding both posts until 1680. His marriage settlement dates to 1664 - he married Jane Steward, daughter of William Steward of Barton Mills. They had seven daughters. In 1675 he was made commissioner for recusants in Norfolk. He had become deputy lieutenant of Norfolk by 1676 and in 1681 he succeeded to his father's baronetcy. The 1677 session of parliament began to show fracture lines between Charles II's court and Parliament. Cook supported Robert Paston in backing the former, making him a potential pro-Crown candidate in the 1679 and 1681 elections. Cook did finally stand for Great Yarmouth in 1685 and won one of its two seats - in the same year he was made a freeman of Great Yarmouth. However, soon afterwards he wrote to William Sancroft, Archbishop of Canterbury: He was appointed to nine minor committees during James II's single Parliament - he was the first man appointed to the committee for the bill for the renewal of the Yarmouth Harbour Act, meaning it was probably he who had introduced it. In 1688 he agreed that some of the laws penalising Roman Catholics and non-conformists might "require a review and amendment" but refused to agree to the abolition of the Test Acts. He was thus removed from his deputy lieutenancy and all other local office in February 1688 and in October that year refused to sit on the bench alongside Roman Catholics. In the post-Glorious Revolution elections of 1689 he was returned for Norfolk and also sat for the county in 1690 and 1698. When the House of Commons had to vote on the House of Lords' motion that the throne was not vacant, Cook voted in agreement. After brief sick leave early in 1690, he returned to Westminster and sat on twenty committees in the Convention Parliament, including ones to repeal the Corporation Act 1661, to inquire into the fall in rents, to adopt new oaths of supremacy and allegiance and to consider abolishing the hearth tax. He also helped consider a bill for bringing in tithes more efficiently and later committees to inquire into disasters during the war and to limit spending in elections. He had to sell Broome Hall and is buried at Cranworth, where his epitaph maintains him as a defender of monarchy "equally unaffected by the wicked artifices of rabid Papists and schismatics". In the absence of any sons or relations, the baronetcy went extinct on his death.
