Finch presided over the trial of John Hampden, who resisted the payment of ship money, and was chiefly responsible for the decision of the judges that ship-money was constitutional. As a reward for his services he was, in 1640, appointed Lord Keeper of the Great Seal of England, and was also created Baron Finch, of Fordwich. He had, however, become so unpopular that one of the first acts of the Long Parliament, which met in the same year, was his impeachment. His estates were sequestrated and he took refuge in Holland. The Great Seal was passed to Edward Littleton.