There is a definite buzz on the quiet line test. I just plugged an old phone into the 'phone' socket of a BT filter.
On hitting the physical mute button on the phone the line does go silent.
Plugged the router into a single power socket, with no extension cables to rule out the possibility of dips in power causing the problem. I checked the Hub stats before I left for work and it didn't disconnect overnight, but upon checking it now, I see it's only keep connected for 4.5hrs, so the problem persists.
I guess it's about time I call BT again, unless there's any more suggestions from you guys?