Baverstock is a surname. Notable people with the name include:
Bert Baverstock (1883–1951), English footballer
Donald Baverstock (1924–95), British TV producer and executive
Garry Baverstock (born 1949), Australian architect, property developer, author and scientist
Gillian Baverstock (1931-2007), English author
Ray Baverstock (born 1963), English footballer and manager