At end of tether, dial up was more reliable!

Question

On Jan 4th my broadband completely died. I reported it and was told that "hopefully the problem would be fixed by Monday 9th.
On Sunday 8th an engineer arrived and spent the whole day sorting out my line................
end result was that he replaced about 20ft of cable from a junction box in my garage to the main socket and told me all was well.
After engineer had left I tried but could not get onto net, my hub (HOMEHUB 2) kept dropping out and was really slow, so much so that I was having to wait 10/15 seconds for a low res Youtube clip to buffer, bearing in mind that prior to Jan 4th we were watching BBC iplayer in HD with no problems.
Yesterday, Monday, I called to report slow speed and was told that it would take a while for the signal to get through due to the new cable.
This morning I carried out a speed test and my result was even slower that on Sunday afternoon.
I called again and was told more works were being carried out and would be completed shortly. An engineer (someone I know,) called within 40 minutes to say that ALL works were now complete and my landline should now be perfect as he had fixed a problem at the exchange.
Carried out speed test........... no change!
Phoned again and was told to hang up so that a line check could be carried out........ an engineer called within 10 minutes and told me that line was nigh on perfect. Carried out speedcheck........... no change!
Called again.
This time I was told that scheduled works were being carried out at exchange, I tried to explain that I'd spoken to an engineer not 20 minutes before who had told me my line was good only to be told that the works were onging and would be completed by midnight. I was told to unplug my hub and not reconnect until after midnight.
It's now after midnight, I've reconnected my hub and carried out a speedcheck, guess what.................. no change!
As of now I have spent over 4 hours either on hold or speaking to someone who thinks I'm an idiot. I have changed filters, I have disconnected and reconnected many times and no change so I've had a gutfull!
This evening I asked my next door neighbour (a good mate,) to carry out a speedcheck on his broadband, here's his result..........
Tonight I carried out a speedtest, here's my result..............
 Here's the details from my hub. Please bear in mind that my connection time is so low because the helpteam told me to completely unplug my hub.
We are both with BT, we are both on Option 3 20Mb broadband, we are both fed from the same box on the same telegraph pole, and presumably the same exchange so why is he receiving 4 times the download speed that I'm getting, but more to the point why oh why am I being fobbed off each time I speak to the BT Broadband helpline?
I really am getting annoyed, someone please help.

Answer 1

Just caried out the quiet line test on a cordless phone (it's all I've got,) and complete silence, good sign?
Over the last few days BT have told me that they have found myriad problems with my line however as of yesterday I was assured that ALL line problems were now solved, and to be honest my phone is now crystal whereas before there was a slight crackle heard during phone calls.
I fully understand that things can, and often do, go wrong but I just hate it when you know that the person on the the other end of the line is feeding you b******t and hasn't got a clue what they're going on about!
This is my 3rd year on option 3 with the 20mb and up until it went daft I was getting between 5 and 6mb download which was fine, although I'mstill puzzled as to how next door can get 12mb???
By the way I've carried out my tests on both master (I only have one socket,) and test sockets with no difference in speed.
As for "bell wire on terminal 3," sorry you've lost me, I am but a simple plumber (relying heavily on my internet to update site, receive emails etc.)
I have 4 copper wires coming into my socket, orange and white are connected the other 2 are cut short and not conected.