BJT Constant Current LED Driver - Inverted behavior?
The circuit diagram looks correct as drawn. 

If you have a multimeter that provides a diode check function, remove transistor Q1 (BC338) and test in both directions (forward and reverse bias) the base-emitter diode and the base-collector diode (see Fig. 1). Ensure Q1's base-collector diode has not failed (short circuit failure mode).

Also remove transistor Q2 and use the multimeter's diode check function to test Q2's base-emitter and base-collector diodes.



Figure 1.&emsp;Pinout for the BC338 and the BC547.