Not sure about the red box being a Master Socket/Line Jack Unit as most are situated within the building (I read on one of the other TB forums that very recent new builds could have a grey waterproof box fitted externally with a master and/or test socket within them).
Do the phone wires to the house/red box come from a nearby pole or are they underground?
Sounds like you don't have an NTE5 master socket which is not uncommon as in various decades newer/different boxes were used.
The socket is probably on the page
here I would think, to enlarge a picture click on it.
If the problem is between the exchange and Master Socket then I would guess that as part of your rental contract Madasafish will contact BT Openreach to investigate the problem.
As long as you carry out the tests as Bob and CS have asked you to do then hopefully your problem with the noisey line will be sorted.
If an BT engineer is sent out to sort a Voice fault it's best not to mention Broadband problems till that Voice fault is corrected as it might cloud the issue.
Alastair
omadasafisho