High-pressure fuel is supplied at a controlled rate to a combustion chamber via a position-controlled valve and a variable-restriction stop-and-pressurizing cut-off valve. A value representative of the real mass flow rate of fuel as delivered is calculated by a calculation unit on the basis of information representative of the pressure difference between the inlet and the outlet of the cut-off valve and of the flow section through the cut-off valve, e.g. as represented by the position X of the slide of the cut-off valve. The position-controlled valve has a variable position that is controlled by the calculation unit as a function of the difference between the calculated value representative of the real mass flow rate and a value representative of a desired mass flow rate.