Cobbett is a surname. Notable people with the surname include:

Anne Cobbett (1795–1877), British author Edward John Cobbett (1815–1899), English watercolour and oil painter Hilary Dulcie Cobbett (1885–1976), British artist Pitt Cobbett (1853–1919), Australian academic, jurist, and editor John Morgan Cobbett (1800–1877), Conservative Party and Liberal Party politician William Cobbett (1763–1835), British radical agriculturist and prolific journalist. Walter Willson Cobbett (1847–1937), British author of Cobbett's Cyclopedic Survey of Chamber Music.