A method and apparatus for controlling a fuel pump assembly comprising a plurality of pump elements for delivering fuel at high pressure to a rail volume, each of the pump elements comprising a plunger which is driven by an associated cam to perform at least one pumping event per engine revolution and a control valve for controlling fuel flow into and/or out of the pump chamber. Each pumping event corresponds to an associated cam lobe of the associated cam. The method comprises, for each pumping event of each pump element, controlling the control valve of said pump element in response to an output control signal derived from at least one previous pumping event. The output control signal is derived by measuring fuel pressure within the rail volume to derive a measured rail pressure value; and comparing the measured rail pressure value with a demanded rail pressure value to derive a rail pressure error. A proportional and integral calculation is performed on the rail pressure error to derive a proportional term for the rail pressure error and an integral term for the rail pressure error. The proportional term and the integral term are combined to derive the output control signal.Monitoring of the integral term for each pumping event of each pump element provides a means for identifying and diagnosing a fault condition within the fuel pump assembly or associated fuel system.