The issues described in this post match mine exactly except they're not as persistent:
The Full Story
We have a single socket in our house where the BT line enters (less than 3 meters from the BT pole) and have always used the test socket, no other internal wiring.
With this setup I had speeds of 3+mbps, which for over 3 miles from the exchange I was happy with,
However for the past 3 years (generally in windy weather?) when we pick the phone up we can hear a hiss/crackle which fades, this in turn allows the ADSL to work faster (or recently sync at all)
I've also used the web based "BT Line Test" as a way to sometimes improve the lines performance as well
We have tried over 10 different filters (and 2 "faceplate" filters) in the test socket over the past 3 years, ADSL and a cordless 4 phone system straight plug into it,
We have tried a range of different routers as well, all behave the same,
We've confirmed the noise persists when using an old basic phone instead of the cordless system
Mixed in with this hissing issue I also had a few months of getting a dropped packet every 10 seconds or so for days/weeks on end, I showed a BT engineer the endless ping logs, from different devices, through different routers, with different phones plugged in and he agreed it looked like a line swinging rhythmically in the breeze (line tests also sometimes solved this for a few minutes or hours)
We've had the same soul destroying experience of engineers visit, plug in their gear, press "test", say its fine, which probably 50% of the time it is, however when its really misbehaving over a holiday period, like Christmas it really rubs it in!
I know fault finding is a pain, especially when its intermittent but I really need some help with what to do now,
The only option I see is getting a second line installed and moving my number to it, which is a bit of a pain but at this point I'm willing to pay for it just to have good reliable access again.