A hydraulic pump (HP; 1), in particular a fuel pump, comprising: - an intake port (IP; 2), - a delivery port (DP; 4), provided for hydraulic connection to a user (CR), - at least one cylinder (CY; 20, 22, 24), movable within which is a corresponding piston (P; P1, P2, P3), wherein the piston has, during the operation of the pump (HP, 1), a reciprocating motion between a top dead centre (TDC) and a bottom dead centre (BDC), - a delivery valve (DV; 26, 28, 30) for each cylinder (CY; 20, 22, 24) hydraulically connected thereto, movable between a closed position and an open position, wherein in the open position the delivery valve (DV; 26, 28, 30) is arranged for enabling a flow of fluid between the cylinder (CY; 20, 22, 24) and the delivery port (DP; 4), and wherein in the closed position the delivery valve (DV; 26, 28, 30) is arranged for blocking a flow of fluid between the cylinder (CY; 20, 22, 24) and the delivery port (DP; 4). The hydraulic pump (HP; 1) comprises a regulation assembly (R; 39, 40, 42, 43, 44, 46) which, when a threshold pressure (p REF ) in a user (U; CR) hydraulically connected to said delivery port (DP; 4) is exceeded, is arranged for keeping the delivery valve (DV, 26, 28, 30) in the open position during at least part of a movement of the piston from the top dead centre (TDC) to the bottom dead centre (BDC) and enabling a reflux of fluid from the delivery port (4, DP) to the cylinder (20, 22, 24).
