Thicknesse is an English surname. Notable people with the surname include:
Cuthbert Thicknesse (1887–1971), Dean of St Albans Francis Thicknesse (1829–1921), Bishop suffragan of Leicester George Thicknesse, 19th Baron Audley (1758–1818), English peer Norman Thicknesse (1858–1946), Archdeacon of Middlesex Philip Thicknesse (1719–1792), English writer Ralph Thicknesse (1768–1842), British politician Ralph Anthony Thicknesse (1800–1854), British politician Viv Thicknesse (1910–1986), Australian rugby league and rugby union player