On 17 January 1770, Cust sent word to the House of Commons that he was too ill to attend.[5] He resigned on 19 January; his successor Sir Fletcher Norton was elected on 22 January. Cust died on 24 January 1770, aged 51.[4] His memorial in Belton church was created by William Tyler RA.[6]
Marriage and progeny
In 1743 he married Etheldreda Payne, a daughter of Thomas Payne, by whom he had two sons and two daughters, including:
Brownlow Cust, 1st Baron Brownlow, 4th Baronet (1744–1807), who succeeded his father in the baronetcy and in 1776 was raised to the peerage as Baron Brownlow in recognition of his father's services.
Elizabeth Cust (1750–1779), married Philip Yorke I (1743–1804) of Erddig House, as his first wife.