LED driver circuit for powering at least two LED strings, each LED string comprising one or more LEDs (D1,D2; D3,D4) connected to each other in series, the circuit comprising: - a positive power supply terminal connectable to the positive pole of a direct voltage power supply generator (Vbat) and a negative terminal connectable to the negative pole of said generator, said positive power supply terminal, when connected to the positive pole of the direct voltage power supply generator (Vbat), being at a power supply voltage; - at least two lighting transistors (TLEDA; TLEDB) and at least two respective driver resistances (RBIN), each LED string being connected between said positive power supply terminal and the collector of a respective lighting transistor (TLEADA; TLEDB), the emitter of each lighting transistor (TLEADA; TLEDB) being connected to the negative terminal through the respective driver resistance (RBIN), each lighting transistor being operable to switch at least between an inactive state, in which said transistor prevents the passage of a driver current (ILED) into said LED string, and an active state, in which said transistor works in the linear zone so as to impose a driver current (ILED) through said LED string, said driver current depending on a driver voltage (Vref) applied to the base terminal of said lighting transistor according to the formula ILED = Vref − VBE / RBIN, wherein VBE is the base-emitter voltage of the lighting transistor, the circuit being characterised by comprising transistor driver circuit means (10,20,40) and in that the bases of all the lighting transistors are connected to the positive power supply terminal through said transistor driver circuit means (10,20,40) so that the driver voltage (Vref) depends in a substantially linear manner on the power supply voltage present on the positive power supply terminal according to the curve Vref = Vx + kVDD where Vx and K are constant parameters, said transistor driver circuit means (10,20,40) comprising - a slope regulation circuit suitable for defining the slope (k) of said curve, and - a curve origin set up circuit suitable for defining the origin (Vx) of the curve. - a positive power supply terminal connectable to the positive pole of a direct voltage power supply generator (Vbat) and a negative terminal connectable to the negative pole of said generator, said positive power supply terminal, when connected to the positive pole of the direct voltage power supply generator (Vbat), being at a power supply voltage; - at least two lighting transistors (TLEDA; TLEDB) and at least two respective driver resistances (RBIN), each LED string being connected between said positive power supply terminal and the collector of a respective lighting transistor (TLEADA; TLEDB), the emitter of each lighting transistor (TLEADA; TLEDB) being connected to the negative terminal through the respective driver resistance (RBIN), each lighting transistor being operable to switch at least between an inactive state, in which said transistor prevents the passage of a driver current (ILED) into said LED string, and an active state, in which said transistor works in the linear zone so as to impose a driver current (ILED) through said LED string, said driver current depending on a driver voltage (Vref) applied to the base terminal of said lighting transistor according to the formula ILED = Vref − VBE / RBIN, wherein VBE is the base-emitter voltage of the lighting transistor, the circuit being characterised by comprising transistor driver circuit means (10,20,40) and in that the bases of all the lighting transistors are connected to the positive power supply terminal through said transistor driver circuit means (10,20,40) so that the driver voltage (Vref) depends in a substantially linear manner on the power supply voltage present on the positive power supply terminal according to the curve Vref = Vx + kVDD where Vx and K are constant parameters, said transistor driver circuit means (10,20,40) comprising - a slope regulation circuit suitable for defining the slope (k) of said curve, and - a curve origin set up circuit suitable for defining the origin (Vx) of the curve. - a slope regulation circuit suitable for defining the slope (k) of said curve, and - a curve origin set up circuit suitable for defining the origin (Vx) of the curve.