if you connect to test socket and any line noise is a problem did you check that all your extension sockets are 'dead' no dial tone when you are connected to test socket?
if extensions are dead when using test socket then you need to report the noise as a phone fault to 151
it is known as quiet line test as with a cordless you can get a dull hum which is normal but qith corded there should be no noise. when using test socket all other socket should not have a dial tone but if you have extensions wired incorrectly and get a dial tone then that is serious problem for your broadband and needs fixed
if upstairs has cordless then the base station must be connected to the extension socket so there should be no dial tone on the cordless phone when corded phone connected to test socket
my cordless phone has a base unit which is connected to the main power supply but is also connected to a phone socket. and when I use my individual corded phone and connect to test socket my cordless phone does not work as the base unit does not get a dial tone