Hi I'm new to the forum but have worked in the tv and comms industry for years, spent a lot of time sifting rfi problems on tv a d radio's over the years, these days it's worse with DVB and more difacult to fully resolve.
This noise may not be one single thing it could be a combination of everything and normally be present on the live line but only one item is perhaps directing it onto the earth or neutral line, something like a heating stat stat could do it if porly installed, even if the mains is off the stat if a manual or battery one would still switch even if the power is off, as has been said the neutral will be isolated when you shut off the main isolator but the earth is not, your house cabling acts as an antenna at such low frequencys. The whole street could be just as bad.
What kind of earth system is your house and street on ? If you had your own rod it's TT. Then you have TNS & TNCS , the last two can make a big difference as for one the earth and neutral combined at the point of entry at your house where as the other has a separate earth back to the transformer then combined there, with the combined earth at your house there are also earth rods added by the DNO at various points on the route from the transformer and these could be picking something up.
One common thing iv found over the years is people often assume that finding the source and stopping it is the solution however often it's not, you would be better trying to limiting its affect on your system, iv recently seen some one replaced the bt incoming cable from the box out side to their phone point with screened cat 6 and earthed the shield, never under estimate ferrite beads on cables, you could also try running your router on 12 battery when the noise is causing the most problems to see if a clean supply helps,(most routers are 12v)
One last though, when the noise is happening have you tried disconnecting your router? Perhaps the noise in on the line it's self ?
Often their is no one solution but a combination of things can improve problems.
