The pump (7) is provided with a body (16) having a compartment (17), and with at least one pumping element (13) that moves in a cylinder (12) in communication with the compartment (17), to raise the pressure of the fuel. The pump (7) comprises fluid-supply means (14, 22) for delivering the fuel to the pumping element (13), and an inlet mouth (26) made in the body (16) and supplied with the fuel coming directly from an external source (2). The inlet mouth (26) is fluidically connected to the compartment (17) to supply it with the fuel in order to lubricate and/or cool the pump (7) itself. Set between the inlet mouth (26) and the compartment (17) are: a non-return valve (33) to prevent in any case the pumping elements (13) from sucking the fuel from the compartment (17) of the body (16); and a flow regulator (29'), which allows an amount of fuel to pass such as to enable proper lubrication and cooling of the compartment (17) and of the parts present in the compartment (17). The fluid-supply means (14, 22) comprise at least one further inlet mouth (24) made in the body (16) and fluidically connected with the pumping element (13) by means of pipes (9).