The fuel pump (10) of a unit fuel injector comprises a pump housing (11) which is of two-part construction and has a pump chamber (14) formed in the housing. The respective parts (11', 11'') of the housing have mutually abutting end surfaces (E1, E2) and the pump chamber (14) is formed in both parts of the housing and extends across the mutually abutting end surfaces (E1, E2).