Regulate current, not voltage.
BINGO!
Where do you put the resistor on a transistor hookup for current regulation? Keep in mind that you will need to regulate from approximately 50 µA (not 0) to 100 mA. Still, not the method that I would recommend.
The resistor needs to go in the emitter side, to regulated the current, which can then be controlled by varying the base voltage with the potentiometer.
Also what's wrong with regulating down to 0mA?
And 100mA is too high for a small 5mm LED.
I hope you don't mind me criticising your (apparently), adjustable 0 to 20 mA (approx), constant current circuit.
But, the way you have drawn it, the 100K pot, will probably not do anything, for around half its travel.
If, you changed it, so that the bottom lug of the pot, which currently goes to ground, was instead, connected to the point where the two diodes meet. Which should be around 0.6 to 0.7 volts.
Then most of the transistors Emitter/Base voltage drop will effectively be cancelled out.
Hence the adjustable pot, should vary over nearly all its range (rather than only half of it).
On the other hand, it is possible, my suggested change may reduce or cause instability. I would have to simulate it, or build it, or calculate hard, in order to find that out.