Old topic. Beating a horse. LDR in place of Potentiometer.

[anotherjim]

Maybe the problem is that you're directly driving the LED, so below its forward conduction voltage (Vf) it's off. With a 0 to 5volt control you lose a large proportion of the range, depending on Vf for that LED. You need a more complex LED drive in that case. Or arrange for a negative supply for the LED cathode adjustable to match Vf so that 0volt control is actually Vf across the LED.
A common emitter transistor could also work reducing the dead part of the control range to 0-0.6volt (which is a lot less than the LED Vf).
It might also work using a single supply op-amp like the LM358 and put the LED in the feedback loop.

[MetalGuy]

It might also work using a single supply op-amp like the LM358 and put the LED in the feedback loop.

It's been done already. Check answer #168 (with pic) :

http://music-electronics-forum.com/t1015-5/