Slow, Slow, Quick? no slow.

Question

I am having broadband speed issues. I will try to cut a long story short but it has now been two weeks and no solution.
I have been a very happy customer with an average speed of 12 to 14Mb/s
Returned from a 2 week break and found that broadband speed was very slow the best being 1Mb/s and at worse 0.15Mb/s. While away we did leave the hub switch on.
Contacted the overseas call center for help and guidance. Got the usual list of things to try and we completed all of the steps, both wireless and wired. A forced reset was to be done and we would soon see a better speed. This continued all week with them ringing up to see how the speed was. During that week each time the same tests, wired and wireless, reset the hub and they would do a forced reset. Also discovered the during the week the broadband would drop out at random times, when the telephone rang or if an out going call was made. At the end of the week we had a lot of line noise. Br Friday I was getting a little annoyed at the whole situation as things were getting worse and no solution was offered. Late friday we were told that an open reach engineer would call Monday and to expect to pay £129:99 as ther was nothing wrong with the line or broadband connection!?!?
The engineer called as promised and could not do enough to help resolve the situation. A thorough check of the line did reveal a few possible problems which were resolved/repaired/replaced. I was shown how much better the line was and the speed I should be getting, 15 to 18Mb/s. I was advised that it may go done as things settle over the next few days.
The speed did infact decrease that very afternoon/evening, back down to 1 to 2Mb/s. Decided to call the help center again but his time we got through to the UK call center. Numerous line tests, hub resets, wired and wireless and to wait 24 to 36hrs. Still no improvement at all. Called them again and a repeat of the tests but no solution. In the mean time we got an IT expert to have a look at our computer. His tests showed up no virus/malware, no start up issues, no conflicts, hardware working and up to date drivers. He carried out a speed test connecting on our hub using his and our computer. They both showed the same low speed.
Called the UK help center again and reported no change and that our computer had been checked out and all appears to be working fine. The reply to this was a dismissive, " well I do not know who the hell he is or what qualifications he has got." Then the usual run of the mill tests, wired and wireless. The BT Wholesale test showed zero up and down load to which we were told that is wrong and the fault has to be with your computer. Not being very happy with the help or what felt like lack of we continued to force the issue of what is wrong and how to fix. It was then mumbled something about line variations and showing peaks and troughs at the exchange but, that would not be responsible for our speed issue. We were told that engineers would be working to resolve the variations at the exchange.
On with the tests results and our findings in the next post due to only allowed 20 000 characters.

Answer 1

Results as promised.
Distance from exchange 560m with no green cabinet, as per open reach engineer investigations.
Quiet line test result, very quiet.
I tend to use speedtest.net for my results as quite often the BT Wholesale times out a lot of the time.
Hub is a type 3
Here are the test results showing last night speed, this morning. Notice the huge increase and then drop like a stone in a short time period.
10/13/2013 8:27 AM GMT    
109.151.113.169   
2.31 Mb/s
0.99 Mb/s   
42 ms
London
~ 50 mi
10/13/2013 8:26 AM GMT
109.151.113.169
2.88 Mb/s
1.00 Mb/s
42 ms
London
~ 50 mi
10/13/2013 7:51 AM GMT
109.151.113.169
17.37 Mb/s
 0.88 Mb/s
46 ms
London
~ 50 mi
10/13/2013 7:38 AM GMT
109.151.113.169
17.40 Mb/s
 0.92 Mb/s
49 ms
London
~ 50 mi
10/13/2013 7:23 AM GMT
109.151.113.169
14.03 Mb/s   
0.99 Mb/s
42 ms
London
~ 50 mi
10/13/2013 7:22 AM GMT
109.151.113.169
13.97 Mb/s
1.00 Mb/s
38 ms
London
~ 50 mi
10/13/2013 7:14 AM GMT
109.151.113.169
17.32 Mb/s
0.89 Mb/s
48 ms
London
~ 50 mi
10/13/2013 7:10 AM GMT
109.151.113.169
17.00 Mb/s
0.95 Mb/s
48 ms
London
~ 50 mi
10/13/2013 7:08 AM GMT
109.151.113.169
17.38 Mb/s
0.93 Mb/s
45 ms
London
~ 50 mi
10/13/2013 7:07 AM GMT
109.151.113.169
14.35 Mb/s
1.00 Mb/s
46 ms
London
~ 50 mi
10/13/2013 7:06 AM GMT
109.151.113.169
14.14 Mb/s
1.00 Mb/s
41 ms
London
~ 50 mi
10/13/2013 7:05 AM GMT
109.151.113.169
13.95 Mb/s
1.00 Mb/s
42 ms
London
~ 50 mi
10/13/2013 7:04 AM GMT
109.151.113.169
14.51 Mb/s
1.00 Mb/s
38 ms
London
~ 50 mi
10/13/2013 6:55 AM GMT
109.151.113.169
17.42 Mb/s
1.00 Mb/s
42 ms
London
~ 50 mi
10/13/2013 6:54 AM GMT
109.151.113.169
17.23 Mb/s
1.00 Mb/s
41 ms
London
~ 50 mi
10/13/2013 6:53 AM GMT
109.151.113.169
17.64 Mb/s
1.00 Mb/s
41 ms
London
~ 50 mi
10/13/2013 6:52 AM GMT
109.151.113.169
17.11 Mb/s
0.99 Mb/s
41 ms
London
~ 50 mi
10/12/2013 9:13 PM GMT
109.151.113.169
1.24 Mb/s
0.98 Mb/s
58 ms
London
~ 50 mi
10/12/2013 8:46 PM GMT
109.151.113.169
1.03 Mb/s
0.93 Mb/s
113 ms
London
~ 50 mi