Cheyne married Lady Jane Cavendish, daughter of the first Duke of Newcastle and had a son, William Cheyne, who became 2nd Viscount Newhaven, and two daughters, Elizabeth and Catharine.
William Cheyne, 2nd Viscount Newhaven (1657–1728), MP for Amersham 1681–1687, 1698–1699, 1701, 1701–1702 and 1705–1707, Appleby 1689–1695, Buckinghamshire 1696–1701 and 1702–1705
William Cheyne, 2nd Viscount Newhaven (14 July 1657 – 26 May 1728) was an English Tory politician who sat in the House of Commons from 1681 until 1707 when as a viscount in the Peerage of Scotland he was required to sit in the House of Lords.
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Wilcote's second wife was Elizabeth Cheyne, daughter of Richard Cheyne of Shurland, Isle of Sheppey, Kent, and Margery Cralle of Cralle, Sussex, a sister of William Cheyne.