A fuel pump includes a pump head defining a barrel in which a plunger is slidable to pressurise fuel in a pumping chamber, and a fluid-inlet path through which fuel flows in to the pumping chamber under control of an inlet valve during a plunger return stroke. The plunger causes pressurisation of the fuel in the fluid-inlet path. The fuel pump may also include a fluid-outlet path through which fuel flows out of the pumping chamber, preferably under control of an outlet valve, during a plunger pumping stroke.