Thanks fungus! Cleared up a few things.
I ran a formula and worked out i should use a 2.5k ohm resistor for the TIP120 running a 1W LED. Does this sound in the ballpark?
What formula, what numbers?
2.5K will probably work with a Darlington but really, it's not critical. The two dangers are:
a) Resistor value too high - doesn't fully saturate the transistor
b) Resistor value too low - lets more than 40mA out of the Arduino pin
The gain of a transistor depends a lot on temperature, voltage, etc. so trying to get it 'perfect' will often cause problem (a).
You're not designing a NASA space probe so it's better to be 100% sure the transistor is fully saturated.
Bit wary of running a led straight off the power supply - so i saw some cheap 1w led drivers on ebay. They run on 12v. Do you think i could switch one of these with another resistor and an external power supply?
A proper power supply is always good but why 12V? I assume the LED runs a 3.6V so dropping 12V->3.6V is a big leap (and creates more heat).
Can you use a 5V power supply? A nice little regulated 5V supply can power both the LED and the Arduino and the drop from 5V to 3.6V for the LED is more manageable.
What I would do,
a) Get a little supply like this one: http://www.ebay.com/itm/140729265471
(nb. I applied my rule of never running eBay stuff at maximum rating, 2A feels about right for this job)
b) Run your LED at 70-80% power with something like this: http://www.ebay.com/itm/310578065040
(nb. I don't know the exact value because I don't have your LED datasheet, but that's probably not far off).
Even better, step up to a 3W LED and run it at 60% power with a slightly lower value 10W resistor.
nb. 60% power usually means about 80% light - LEDs produce more heat than light when you get near their limits.
(all eBay items picked at random, I don't know the sellers)