BT vs broadband provider conflict

Broadband provider says it's not a broadband fault, BT OpenReach says it's a cable fault, BT retail says there is no problem. Any advice on how to knock 3 heads together and have a broadband service restored?

We need to know the ISP, the broadband product, and the details of the problem. Also who your phone line rental is with.

"BT OpenReach says it's a cable fault,"

who told you this ? if OR say you have a cable fault that needs to be fixed then see how things go.

Who is your broadband provider?

If Openreach have found a cable fault, given they maintain the cables seems it is right for them to fix it.

We need some more background to judge things properly

Thank you for all the replies. Apologies, it has taken all day to get the page to load and supply more info. Broadband is from Freeola and line rental is from BT.
The problem:
The noise margin periodically starts fluctuating between 5 and 6 dB and the connection speed keeps dropping to zero. There is no observable pattern to it. Sometimes it remains OK for about 8 minutes.
We have repeatedly been told by BB provider that "the problem is within your premises", "the problem is with your equipment" or "the problem has been resolved according to BT".
Timeline:
4th January, 2012:
We lost our phone service completely.
5th January:
A BT engineer visited and identified a cable fault. He found a spare pair in the cable and swapped it over. This restored voice service, but failed to give a stable internet connection. We were advised to wait 10 days for the line to stabilise. It didn't. This may be coincidence.
February, a few weeks ago:
An OR engineer visited. After extensive investigation, he diagnosed a fault in the last span of the cable. He apologised that the cable probably could not be changed until a few days later, and that the old pole might well need to be changed as well.
Nothing happened, nobody rang, nobody came.
Our broadband provider advised us that, according to BT, the issue had been resolved and that was the end of the matter. We were told that, although we had not noticed the cable being replaced, it had been replaced, and there was no longer a fault.
25th February:
An OR engineer visited. He again confirmed that there was no fault within our premises, as was continually being claimed. He guessed that the parameters had probably been reset remotely just before he came. While he was there, the router was connecting at speeds about 2-3 times faster than we are used to and was stable. The line tested OK. He further confirmed by visual inspection that the span had clearly not been replaced. While he was still there the line briefly lost sync and, after he left, rapidly deteriorated to its original state.
Tests and checks:
A QLT is always OK.
After the basic checks and remedies, we plugged the router directly into the test socket.
The problem was still there.
We swapped out the router and plugged the second router directly into the test socket.
The problem was still there.
When nobody would accept there was a problem, we bought a further two routers.
These last two have reputations of being able to hold onto the line at low noise margins.
We have now tried 4 different routers into the test socket. The problem is exactly the same.
I hope I haven't given too much detail now

In reply to a post by dibsmft:

When nobody would accept there was a problem, we bought a further two routers.
These last two have reputations of being able to hold onto the line at low noise margins.
We have now tried 4 different routers into the test socket. The problem is exactly the same.
I hope I haven't given too much detail now

which routers?

Lots of words but little detail

For the routers you have used what the connection speed, attenuation and noise margins.

The noise margin swinging between 5dB and 6dB is no evidence of a problem at all, since this is perfectly normal. If we can see those numbers from when its both good and bad we can advise.

The responsibility for any broadband fault lies with Freeola.

Netgear DG834G and D-Link DSL-G604T as recommended by Kitz dot etc.

Thanks. The attenuation is constant at 58dB. I've managed to get graphs of connection speed and noise margin uploaded:
http://escapetothecountry.info/Broadbandgraphs.doc
These are from after the last OR engineer left. I have never before seen connection at such a high speed as when he was there. The connection is now never 'good', it varies from unable to load a web page, to 30mins to load a page, to a minute or so.
These are some reults from this morning.
Packets lost Average latency Jitter
24% 22.077ms 1ms
2% 22.031ms 1ms
0% 22.892ms 6ms
4% 23.93ms 8ms

Can you get some finer graphs ... take the sample interval down to 10 seconds or less ... and set the Noise Margin scale Y axis at 0 to 6.

From the graph, it looks as though your router decides to do a resync as soon at the SNR drops below 6 which would be a little odd and I am wondering if the margin n goes any lower than 5.