Sounds to me like "Image" channel interference...
Although alarm clock radios are not the best receivers and interference from strong transmissions are quite likely. Civil ATC Transmitters are restricted to 5W at the antenna. Military can go up to 100W but are mainly in the UHF 240-400MHz band but can be on the VHF band of 118-138MHz and should be no more than 20W.
Basically they are "blasting" there way through the receivers.
Way to get around it?
Get a DAB radio!
You can listen to the Six Music that's much better than Radio 1
