You can add RFI filters onto the power cables, but this really shouldn't be necessary. Fluorescent lights which interfere that badly are probably faulty. See if you can tie down the problem to one particular fixture. If so, then you should get it replaced.

If it just seems to be cumulative from all of them together, then you could try RFI filters on the main power cables but I'm not sure it will solve your problem. Your best bet would be to get better quality fixtures. If you have the radio on the same mains circuit as the lights then that is a good candidate for the filters. Or you could just try it on batteries or a different circuit. Long cable runs to the speakers can also make good aerials!