Radio Interference from Lights

[Lee S]

My radio sounds sweet as a nut until I turn on the lights. Side-lights or main lights. I don't have HIDs but do have LED side-light bulbs and LED number plate bulbs. It's as though the reception takes a real drop. The radio is still audible and listenable, but there is what appears to be background static/interference/mush. Turn the lights off and it's perfect again.

Any ideas? Could it be the LEDs? Bad earth or dirty connection on one of the bulbs?