A high pressure pump assembly (HP pump, 10) for a fuel injection system of an internal combustion engine, the pump (10) comprising: a high pressure unit (HP unit, 14) extending along a main axis (AA) and comprising a foot portion (16) adapted to cooperate with a rotating cam (32) to engage a pumping plunger (24) in a reciprocal axial displacement and, a pumping head (18) having a housing (26) provided with a compression chamber (34) wherein, in use, fuel enters at low pressure via an intermediate inlet conduit (36), then is pressurized by the pumping plunger (24), then exits at high pressure via an HP outlet (38), characterized in that the high pressure pump (10) further comprises a low pressure unit (LP unit, 12) having a connecting member (20) adapted to fixedly receive a valve (28), a general pump inlet (22) for receiving LP fuel from a LP tank, the connecting member (20) being further adapted to cooperate in a complementary engagement with the HP unit (14), said engagement being angularly indexed.