During the Popish Plot, he played an active part in the interrogation of witnesses and preparation of the Crown's evidence. He is said to have been somewhat sceptical about much of the evidence, and drew up a private report referring to the difficulties with Titus Oates' evidence. In general he behaved with moderation and restraint during the Plot, as shown most notably in his impartial conduct, as Lord High Steward, of the trial of William Howard, 1st Viscount Stafford,. Kenyon notes that during the examination of the informer Miles Prance, Finch threatened him with the rack, but such a lapse was most uncharacteristic of Finch, who was a humane and civilised man; in any case the threat could hardly have been serious since the use of the rack had been declared illegal in 1628.
The original early 17th-century building was constructed in the village of Kensington as Nottingham House for the Earl of Nottingham. It was acquired from his heir, who was Secretary of State to William III, in 1689, because the King wanted a residence near London but away from the smoky air of the capital, because he was asthmatic. At that time Kensington was a suburban village location outside London, but more accessible than Hampton Court, a water journey on the Thames. A private road was laid out from the Palace to Hyde Park Corner, broad enough for several carriages to travel abreast, part of which survives today as Rotten Row. The Palace was improved and extended by Sir Christopher Wren with pavilions attached to each corner of the central block, for it now needed paired Royal Apartments approached by the Great Stairs, a council chamber, and the Chapel Royal. Then, when Wren re-oriented the house to face west, he built north and south wings to flank the approach, made into a proper cour d'honneur that was entered through an archway surmounted by a clock tower. Nevertheless, as a private domestic retreat, it was referred to as Kensington House, rather than 'Palace'. The walled kitchen gardens at Kensington House supplied fruits and vegetables for the Court of St. James's.
Personal life
On 30 July 1646, he was married to Elizabeth Harvey, daughter of William Harvey's younger brotherDaniel, and his wife Elizabeth Kinnersley. Together, Elizabeth and Heneage were the parents of five children, including:
According to the Encyclopædia Britannica Eleventh Edition, his contemporaries of both sides of politics agree in their high estimate of his integrity, moderation and eloquence, while his abilities as a lawyer are sufficiently attested by the fact that he is still spoken of as the father of equity. His most important contribution to the statute book is The Statute of Frauds. While attorney-general he superintended the edition of Sir Henry Hobart's Reports. He also published Several Speeches and Discourses in the Tryal of the Judges of King Charles 1. ; Speeches to both Houses of Parliament ; Speech at the Sentence of Viscount Stafford. He left Chancery Reports in MS., and notes on Coke's Institutes.