Leavenheath is a village and civil parish in Suffolk, England, close to the Essex border. Located on the A134 between Sudbury and Colchester, it is part of Babergh district. The parish also contains the hamlets of Cock Street and Honey Tye, and in 2001 had a population of 1,373, falling slightly to 1,370 at the 2011 Census. The village was named after the Leaven Heath, an area of open land between Boxford, Bures, Nayland and Polstead.