Robert is probably right, but moving or rotating the radio might help. An AM radio has a directional antenna, and maybe the interference can be nulled out, and/or weakened by moving further from the source.
FM and DAB work from a whip antenna, and it may be possible to replace it with a coax fed external antenna on the roof. These pick up much more signal and far less interference; great apart from the cost and hassle.
If the radio is portable, worth moving it close to each LED lamp in turn to confirm they are all faulty. Possible that the suppression on one lamp has failed and the others are OK.
Worth a try, I’m not optimistic though.
How about an internet connected speaker, or an MP3 player?
Dave