AHEM.
With cable, in Milton keynes, everyone thought ADSL would work a treat until it was realised the BT put Aluminium cables in instead of Cooper on most of the new estates.
The thing with line noise is that it happens all the time, and the line is always crap, it's doesn't tend to come and go, it's either there or not, and doesn't fluckuate very much....unless the conduit gets flooded or something..

With Intermitant Problems, you will find it can depend on what's actually going on at BT, and whats going on at the ISP, often not a great deal, but here is a good way to test.
With ADSL (Broadband) you have two servers that Authenicate you.
You have a BT one, and an ISP one.
Your username will look something like; blahblah@isp.com
Ok, the simplified Proccess in order then.
Your Modem/Router from your ISP will talk with the BT Authentication Server first (RADIUS normally) and that server will look at your "@isp.com" bit of your username. This then tells the big AS Series ATM Routers at BT to route you traffic to your ISP (Virgin.net)
Then Virgins job is to Identify the "blahblah" bit of your username (Using RADIUS Again).
Only when that is done will you get you IP Address for the Internet, and be allowed to surf.
How does this help you?
Well you can often find out where the problem lies by doing a bit of testing.
Change your Username to BT_User@Startup_Domain.
Password Blank or Password. (Sorry it's a long time since I worked on the Broandband Helpdesk)
You will NOT be able to browse the internet witjh this, but you WILL be able to log in.
If you cannot log in, the problem is with your Line, either at the DSLAM (Digital Subscriber Line Access Multiplexer) not unheard of to have ports just die to be honest (especially in Fujitsu DSLAMS), or the line card at the Exchange, again not that uncommon....
If you can login, this proves that the Line is fine, and the Connection to the BT side of the Network is fine.
Disconnect and change your usename to BT_User@<isp.com>
Password Blank or Password - Virgin may have changed the password, so it might be worth asking them what it is.
If this fails your Problem is with Virgin Internet RADIUS Server, probably over subscribed (by 45% normally, hence those lame arse download limits and DPD kill signals)
I suspect the first one will fail, if you try it while you are having problems.
From what you have said, it seems as though the DSLAM is not handling the load very well, and it may need replacing with a real one....From Cisco... not Fujitsu..!!!

Cheers.
Matt