Remove the TL431 for a moment to test the circuit. The LED should light.
Current should flow though R1 and turn on Q1, so that more current is available to flow though R5 to light the LED.
If the LED does light, go to (X) below.
If the LED does not light with TL431 removed, bypass Q1 (collector to emitter) with a wire. If the light now lights, you've got R1 or Q1 wrong. If the led does not light, it's faulty, the wrong way round or R5 isn't connected, the wrong value or faulty.
(X)
Connect the bottom of R1 to ground with a wire. The LED should go out. If not, you have Q1 fitted wrong or it's faulty.
Assuming now that the LED lights, and goes out when you short R1 to ground, the problem lies with the TL431.
Replace the TL431, and remove the potentiometer. Connect the reference input of the TL431 to ground, and the light should be on. Connect the reference input of the TL431 to the cathode and the light should be off. If that's not working, you've got a faulty TL431 or it is wired wrong.
Once that works, connect the potentiometer. If the LED is on all the time, R8 is too big or not connected, or R6 is too small or shorted.
I hope this gives you some clues.