I would bet my life that the problems an extension.

It could be something really tricky to solve. Eg the bad extension may be unfiltered and run along side mains cables in the walls. This often causes significant interference.

It's probably easier to either

1) disconnect the extensions
2) try a filtered faceplate assuming you're using the master for BB - this MAY help but isn't guaranteed

Just to check does every extension have a filter plugged in?
Is anything plugged into the extensions slightly fuzzy when the broadbands active?

It could just be that one of the filters at an extension socket is faulty or something at an extension is unfiltered