Wow, thank you guys for going through this so thoroughly! So, based on what you've said I'm now looking at this generic 220Ω resistor and this 5kΩ logarithmic pot(0.5W rating).
wayneh, that graph looks fantastic. If I can get anywhere near that level of linear brightness control I'll be delighted.

Do you wish the LED to go off completely?

This would be very nice to have. I can't seem to see whether the pot I linked to above has an "off" switch though. Can I achieve this with the circuit as is?

Do you know about the specific battery you plan to use?

I was just going to use a basic Duracell 9v battery. Is it ok? Also, would you guys recommend using 9V battery snap connectors (not sure if this is the technical term), these things here:

 

A 9v battery and that battery clip is what we all had in mind.
If you connect everything in series the LED will not go out.
If you connect as I suggested it will go out.
Any reason why you switched from 10kΩ to 5kΩ pot?
It works ok too but it will draw more current.

I will compare a linear pot with a log pot and get back to you.

 

If you connect as I suggested it will go out.

I agree. There's a small penalty of using a bit more current but squeezing efficiency is not the issue in this application.

Any reason why you switched from 10kΩ to 5kΩ pot?

It gives a more linear profile than the 10K, which was ballparked by me as a way to get to low brightness at the extreme. Your circuit eliminates the need for that concern. Waste current draw is less than 1 mA.

 

I agree. There's a small penalty of using a bit more current but squeezing efficiency is not the issue in this application.It gives a more linear profile than the 10K, which was ballparked by me as a way to get to low brightness at the extreme. Your circuit eliminates the need for that concern. Waste current draw is less than 1 mA.

So if I want to be able to switch the LED off I should use MrChips' circuit and go back to the 10k pot? Will I still get a relatively linear brightness response?

 

Ok, I tried with both 10k linear pot and log pot.
Because the log pot gives better control at low resistance range, it would be better to reverse the connections on the pot. Hence turn fully clockwise to turn off.
(The other solution is to use a pot with reverse log taper.)

The simple solution is to go with a 10k linear pot.

 

Ok, I tried with both 10k linear pot and log pot.
Because the log pot gives better control at low resistance range, it would be better to reverse the connections on the pot. Hence turn fully clockwise to turn off.
(The other solution is to use a pot with reverse log taper.)

The simple solution is to go with a 10k linear pot.

Ok, I think I'll go with a 10k log pot (probably this one) then and reverse the connections.

 

Ouch! That seems rather expensive. Shop around.
Check JM77J or FW22Y from Maplin.
http://www.maplin.co.uk/components/resistors/potentiometers

 

The 5K log taper will give a more linear result (compared to 10K) of current vs. % rotation. A 1K or a 10K would work fine but both give a less linear result. All 3 would work fine in the circuit suggested by MrChips that allows the LED to go fully off. The 1K would waste more current, which is barely an issue with the other 2.

 

The 5K log taper will give a more linear result (compared to 10K) of current vs. % rotation. A 1K or a 10K would work fine but both give a less linear result. All 3 would work fine in the circuit suggested by MrChips that allows the LED to go fully off. The 1K would waste more current, which is barely an issue with the other 2.

Thanks. I ended up going with that 10k log pot from radionics, I know it was expensive but it was the only log one I could find that was rated above 0.2W. I also got some 220Ω resistors, got the LEDs I linked to earlier and got these 9v battery clips. Hopefully it all arrives early next week.
So, my circuit should end up being:

1) +ve battery goes to 220Ω resistor, resistor to top end of pot (terminal-3).
Bottom end of pot (terminal-1) goes to -ve battery. LED anode connects to wiper of pot (terminal-2), LED cathode connects to pot terminal-1 or -ve battery.

This will let me turn the LED off, won't it?

 

This will let me turn the LED off, won't it?

Yes, it will. I'll be curious to hear how this works for you.

 

Just a quick update - the parts arrived the other day but I only got a chance to test them earlier today. Seems to be working very well, the LEDs are very bright which is great and the pot is giving a nice almost-linear variation in brightness over the course of the turn. For testing, I was just going from:
battery+ -> 220Ω -> pot terminal1 -> pot terminal3 -> LED anode -> LED cathode -> battery-,
so I didn't get to test turning the LED off, but that should work fine too.

The plan is now to stick the LED to a bit of stripboard, run some recycled coax cable from that to the actor's pocket, where the battery, resistor and pot will be housed in some sort of container. The container's the only bit I'm not sure about now. It needs to be something small enough to fit in a pocket, with a way for the pot control knob to stick out, and fairly robust to movement and tugging. I was thinking of encasing the parts in a blob of silicone glue like Dan Goldwater's power LED circuit. Any thoughts?

 

I use Altoids tins for many such things. You can close the lid when the build is done, and the metal walls are tough enough to mount small switches, adapters, etc. Pocket sized, fairly rugged, free (as long as you like Altoids!). Just remember to leave to leave room for the metal lid to close, and be sure to insulate against small deformations.