I'm not an expert on the design of LED lights but I do spend a lot of time tracking down this sort of interference. Assuming the interference is caused by a switching power supply in the lights, your problem is most likely conducted noise through the power line and would be corrected by the filter. Radiated noise would typically interfere with specific channels rather than the wide spectrum you described.
Problem is, conducted noise can radiate out of the power lines so filters are typically located near the noise SOURCE rather than the device affected by the noise.
There are several easy ways to filter the power line at the source but these depend very much on the nature of the interfering signal. If the problem exists when just a single lamp is on, try the filter you mentioned above. It's possible it will work when installed at the breaker panel on power lines to your radios but it's most likely that you will need to place them at the LED lights themselves.
As Tim R stated, the cheap items would tend to cause more of a problem.
