A fuel pump for use in an internal combustion engine comprises a pump housing provided with a plunger bore, a pumping plunger which is movable within the plunger bore by means of a cam drive arrangement to perform a pumping stroke to pressurise fuel within a pumping chamber and a cam follower arrangement interposed between the cam drive arrangement and the pumping plunger so as to transmit a drive force of the drive arrangement to the pumping plunger. The cam follower arrangement includes a timing advance piston for advancing or retarding the timing of the pumping stroke, and control means for controlling the timing advance piston so as to advance or retard the timing of the pumping stroke. The timing advance piston is provided with a groove on its outer surface for receiving fluid, thereby to provide a centralising force to the timing advance piston, in use. The cam follower arrangement advantageously includes an advance piston spring which is housed within a spring cage received within a lower portion of a return spring for the pumping plunger.