The problem is probably coming from the circuit driving the LED, if it's a modern LED driver it works by pulsing the LED on and off, changing the pulse width to give the appearance of being 'dimmed' or 'brightened', however the probem with this is when any electrical circuit is turned on or off, the transient stage between off and on creates a broad band pulse of radio noise, and potentially the same happens when it is turned off. Two solutions: Buy an LED lamp that does not cause this problem, or modify the existing lamp, if you're able to.
A very small value ceramic capacitor across the supply to the LED may just be enough to reduce the noise without affecting the operation of the lamp, too big a capacitor and it may just cause the lamp to run too bright, or worse. Personally I'd just get a different lamp.