If the noise is still there with the home hub turned off, then you need to report a noisy phone line.
From what you have described so far, it sound like your internal wiring is incorrect.
There should be dial tone on the test socket, and no dial tone anywhere else once the botton section of the NTE is removed.
If you refer to my last diagram, that will show how things should be wired.
I think you are going to have to request a visit.
Very pleased to share than a BT Engineer unexpectedly turned up this morning; I was in contact with BT's helpline last night and they arranged to just ring me today to talk about the problem, but clearly have escalated it and were able to arrange a visit this monring.
Turns out whoever put in the phone/ADSL for the previous home owner (elderly lady so very late to get it, circa 2006/2007), the master socket was upstairs but someone put an ordinary socket face on that one, and a master socket face on the downstairs socket, which was ALSO a master socket (!). This is why when trying to use the downstairs test socket, I got no dial tone. For some reason someone had wired master socket (1) > master socket (2) > extensions when they put the phone and ADSL in for the previous home owner.
I'd taken (2) to be the master socket due to it's appearance, and based on evidence - (2) was where the BT wiring was coming into the house from outside.
So the Engineer killed the one upstairs and bypassed it, made (2) the true master socket and put in a new filtered socket, no more messing with microfilters.
The result -
Thanks to everyone who helped on here, very grateful for your rapid and informative assitance.
Thanks to the Engineer who came out and rectified it all very quickly.
And thanks and well done to BT for getting someone round the next day. Very impressed!
Now, to work on getting that 34.4mbps up to 39.9mbps......