A fuel pump comprising a first pumping plunger reciprocable within a first bore and defining, with the first bore, a first pumping chamber. A second pumping plunger is reciprocable within a second bore and defines, with the second bore, a second pumping chamber. The fuel pump further comprises a supply passage, whereby fuel from the first pumping chamber is supplied to the second pumping chamber. A drive arrangement is provided for driving the first and second pumping plungers in both an extending direction and a retracting direction such that when the drive arrangement drives the first pumping plunger in its retracting direction, the second pumping plunger is driven in its extending direction to expel fuel from the second pumping chamber, and when the drive arrangement drives the first pumping plunger in its extending direction, the second pumping plunger is driven in its retracting direction and fuel is expelled from the first pumping chamber through the supply passage to the second pumping chamber.