@Dimitris, I think the point of @mike-wsm was that spectrum analysis/scope of the audio might give an important clue to the noise source....you got a piece of rotating machinery with dodgy brushes/a spark etc, you're going to see some big spikes proportional to its RPM. Also remember that RF doesn't start in the MHz...radio 4 is still on LW @ 192kHz! It can go MUCH lower than that...
Sure it would be really nice to sniff the actual RF spectrum near the antenna, or the power leads etc too. I have just the portable 5GHz analyzer for the job..but it's not the kind of gear most people have to hand.
It's also important to realize that a great many noise problems are not "in band"..that's is in the frequency range the radio is tuned to receive signals at. The RFI finds it's way into internal circuits that are tuned to work at other typically much lower frequencies and get's mixed in with the real signal there. This noise MIGHT be VHF wideband (i.e throughout the 118-136MHz bands) but very likely it's not (handheld not hearing it was a big clue), it's probably something much narrower band and of much lower frequency.
Hopefully the next batch of experiments disconnecting the coax etc will tell us what path the noise takes into the radios and well be able to eliminate some of the many good suggestions we have.