Ante,
How powerfull is this light?
I think you'll need a lot more than 30 turns on the secondary or more on the primary, a red LED needs 1.9V to light up and for this to happen the amount of turns on the secondary needs to be a sufficiently high ratio to the voltage drop caused by the current on the primary.
Here's an example:
The mains light requires 500mA.
Suppose the torridial core with 10 turns has an inductance of 100uH (and that's being optimistic), the impedance @50Hz will be:
2pi*50*100*10-6 = 0.0314ohms
The voltage drop on the primary @ 500mA will be just:
0.0314 * 0.5 = 15.7mV
If the secondary has 30 turms the out put voltage will only be:
3 * 0.0157 = 47.12mV - way to low to power an LED!
The voltage needs to be at least 1.9V to light the LED that's 1.9/0.04712 = 40.32 times higher to power the LED so the number of turns on the secondary will need to be:
40.32*30 = 1209.7, off course I wind a few more to ensure the LED will glow birght enough as it's forward voltage needs to be above 1.9V.
If you don't fancy winding this many turns than I recommend you wined more on the primary.
Note:
These calulations don't take into account the fact that the core might saturate or the DC resistans of the turns on the secondary.