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His daughter was Mary Anne Whitby, his son was William Symonds, Surveyor of the Navy, and his grandsons included William Cornwallis Symonds, Thomas Symonds, and Jermyn Symonds.
In the 1660s Lady Batten, wife of Sir William Batten, Surveyor of the Navy, had a vineyard at their estate at Walthamstow; Samuel Pepys thought the wine (which was red) "very good".