Are you by any chance using retro-fit "micro" LED (for example cooker lamps in G4 capsule), or MR16 12V replacements for halogens? Both these, and potentially other similar combinations will use LED lamp A with transformer/driver B, and are the type most likely to be a problem.
For example I've come across issues with G4 capsules and with G9 capsules, with MR16 LEDs and with el-cheapo ebay flat ceiling tile lights.
The manufacturers of the lamps, if they are from a reputable mainstream brand, (yours might be brandless Ebay ones, you didn't tell us), would nonetheless make EMC tests during development. These tests would probably supply the lamp from a standard nicely regulated and filtered power supply. In the field, the unknown "combination" of lamp + driver wouldn't be available to test since it would be unknown. Matching the undefined output impedance of a unknown transformer at ~100MHz, to the undefined input stage of a miscellaneous lamp can easily lead to radiated emissions in the VHF band well outside "legal" limits, - and screw up your radio nearby.
Those LED's which are monolithic, incorporating the 230V driver and electronics (a standard mains light bulb or a mainstream brand integrated downlighter for example) will have been EMC tested in their entirety, and will have met minimum emissions standards. Hence I'd be surprised if it were one of those. (Unless the source were a grey import, perhaps fraudulently CE marked, there are many).
We have a lot to thank the European Union for, and a big one is product testing and CE marking. - What the hell will happen when the floodgates open to the world supply of crap is really unknown.. but I digress.
Just because your lamps have been tested to a standard, and potentially passed, does not mean there are "zero" emissions, but that the emissions are at a level which is deemed - usually- to be not a problem.
Several ways are possible that even good equipment might fail, and faulty manufacturing could easily bring this about if incorrect filtering or other components were fitted. This wouldn't necessarily prevent the lamp from working "normally".
Fixing it? - You are on your own, and finding the right sticking plaster- if one exists could be very time consuming. I have in the past experimented with decoupling and ferrites on leads, but in this regard have had relatively little success.
I think the lesson is to always buy from mainstream quality manufacturers and take them back if they are interfering with your radio!