A vehicle braking system includes a master cylinder. In a delivery line of the master cylinder there is a pressure transfer device, which generates a pressure in a hydraulic actuating line of a respective brake device following a fluid pressure communicated to a first inlet of the pressure transfer device from the delivery line and/or following a fluid pressure supplied to a second inlet of the pressure transfer device from an electrically-operated fluid pressure source. An electronic controller controls an enabling/disabling solenoid valve, and the electrically-operated fluid pressure source to create different operating modes of the system. The system does not include any vacuum-operated servo-assisting devices. The master cylinder is associated with a hydraulic device for adjusting the feeling on the brake pedal, in which a fluid pressure is generated that opposes the brake pedal actuation. The electronic controller controls the pressure in the device for adjustment of the feeling on the pedal.