A Tale of Woe --- Infinity Installation

Question

It's now over a month since I originally ordered infinity and telephone with BT, and I have neither - both have never worked at all. There have been multiple failings on the part of BT, from two engineer visits (who failed to properly document the fault) and the technical faults team (who did not listen to me, did not record information properly and did not properly assess the fault).
I've been very patient and polite throughout the whole endeavour; however I’m now being told that I have to wait another month to have my broadband and phone line installed. This is not acceptable, and is over 2 months since I originally ordered! If BT had listened to me, or functioned in any type of efficient manner, my situation would now be resolved. I can't even find the correct place to document a complaint, so public is always best.
Timeline.
14/12/2013. Ordered Unlimited BT Infinity 2 and phone line. THIS IS A COMPLETELY NEW INSTALLATION. We had just moved into a new property, and have NOT had a broadband or telephone connection before at a previous property.
24/12/2013. Engineer arrived to install broad & phone. He failed to get anything (either phone line or broadband) working. He said that there was an issue with PCP. The line had been set up on the incorrect "green box" - one that was over a mile away, instead of the box just down the road from us. He said, it looked as though the line had been transferred from the previous owners to us, instead of being set up new. He said that he would report this back to BT, as it required an Openreach engineer to sort it out. HE DID NOT DO THIS.
27/12/2013. I called BT, and went through an automated system. This tested the line and found a fault on the line, generating an automated response for the fault on both the phone line and the broadband.
27/12/2013. I called BT again, as I was sure that I should explain what had happened with the engineer (and explain the problem with the PCP) - I was confident that the automated system would not be enough to get this problem fixed in the most efficient way. I was told that a general fault had been found in BT's network, and that it would be fixed on the 06/01/2014. Instead of listening to me about the issue with the PCP (which had been explained to me by the engineer), the CSO bluntly refused to take the issue further, stating that it was a "general problem in BT's network" that would resolve my issue once dealt with. As above, this is NOT a BT network problem, it is a problem that is specifically to do with the property and how it's been routed. I was told that if it did not resolve the problem I would be entitled to "compensation" - which I am now due. I specifically asked the CSO to make a note of this on the file.
02/01/2014. The Broadband fault was closed with absolutely zero feedback to myself or anyone looking into it.
02/01/2014. I contacted BT via chat so see why the broadband fault had been closed when it was not working. I was told that the broadband would not work with the phone line error. No explanation as to why it had been closed was forthcoming. CSO was blunt and unhelpful.
06/01/2014. The Openreach engineer arrived. Lo and behold, he told me EXACTLY the same thing as the previous engineer - the whole set up from the beginning was incorrect. We have been set up on the wrong PCP, and the line needs to be set up again from the sales end. He did a 5 minute line test and then left. I had to wait 10 days, for a 5 minute chat to tell me something that I already knew, and that, had the CSO I spoke to on the 27th listened to me, would probably be fixed by now. THE ENGINEER DID NOT REPORT THIS.
07/01/2014. Once again it was up to me to contact BT to have the matter resolved. Spoke to tech help and requested that this matter be looked into urgently. I was told that the engineers marked the fault as fixed – contrary to what the engineer himself told me yesterday. Apparently this “fault” needs to be sent back AGAIN to the engineers to get reinvestigated, and I would be contacted in 24 hours. I said that I would like to hear back within one hour (as I just keep getting fobbed off), and the CSO “Ratna” agreed that I would be contacted at the time specified today by them or their supervisor. The call-back came (2 hours late), which was then apparently too late for the CSO to contact the relevant team and hear back from them today – so they will be calling me tomorrow. BT has now agreed that there is a “cabling issue”.
08/01/2014. Had a call from BT at 1pm today – unfortunately this was during my lunch break and I missed it. No message was left to inform of what it was regarding, or what the call-back number was.
08/01/2014. Spent half an hour in a queue waiting to speak to a chat agent only to be told (when I reached number 1 on the queue), that the session had been cancelled as there we “no agents available”
08/01/2014. Went through the chat queue again however Ratna had apparently gone home for the day, so I spoke to Sanjog instead. I was then told that the engineers need more time to check the fault and that I would get a call back tomorrow. Sanjog then proceeded to reject the “cleared” mark on the fault (again?), and tell me that the engineering team close at 5 so he would be unable to contact them now. 
10/01/2014. Didn’t get a call back yesterday, so spoke to chat again today. I was told that the line was connected to the wrong distribution point (as I told the BT on the 27th December), and that the technical faults team would be unable to deal with it. I was then told that I would need to speak to customer options, and that they would need to place a new order for the line. The CSO on chat, then called me to transfer me to customer options. After about half an hour on hold, I spoke to the same CSO, and was told that customer options would actually be unable to deal with it, and that she would need to send an email to the engineers and that they would be contacting me directly today.
10/01/2014. Spoke to the sales team this afternoon who went through the process of setting up a new order. I was told that I would need to wait until the 27th January for the engineers to come out to install the new line. Half way through setting up the order I was put on hold and the line cut out after about 10 minutes.
10/01/2014. I expected an immediate call back to complete the order however this did not occur. Instead, it was left up to me to call back and spend an hour on the phone trying to find someone to complete the order. I eventually found the same operator who completed the order for me. I was then told that I would need to wait until 25th February 2014 for the new line to be installed. I said this was not good enough (and she agreed) as it was nearly a month since placing the original order, so she sent an “email” to her manager, who would call me back to arrange a much closer date for the installation.
14/01/2014. I never received a phone call from BT, so it was once again up to me to call and explain the same thing again, to try and have someone bring the installation date forward. I spoke to order management who (once again agreed) that the time I had been waiting was beyond ridiculous. So had to “email” an escalation claim to OpenReach in order to try to get that date pushed forward, which she did.
16/01/2014. I actually got a call back from BT! However, it was simply a rejection message “All engineering resource in your area has been allocated to work on repairs to the network as a result of the recent bad weather across the uk”. So they were unable to bring the date of the appointment forward. I find this hard to believe that BT cannot spare one engineer for < 1 hour to install a new line for me, given the huge amount of time it’s taken to get to this point.
Summary of Failings:
I was told what the issues were by two separate engineers. A new line had to be installed to the nearest PCP by placing a new order with sales. Neither properly documented this with the faults team or followed up on what needed doing. It was left up to me to try and explain.
The faults team categorically dismissed everything I said, and did their own thing. By following that processes, it took over 2 weeks for the original fault with the line to be discovered. If either the engineers had properly documented the faults, or the faults team had listened to me at the very beginning of the process, the new line would have been set up, and I would now have broadband.
On multiple occasions I did not receive call-backs that were promised and it was left up to me to contact BT. This was a failure on all fronts, technical support, engineers and sales were all supposed to call me at some point, including management, supervisors and CSO’s. This is a failure from bottom to top.
All correspondence between different teams appears to have been completed via email. I asked on multiple occasions to have the matter resolved there and then, and was always told that it would take 24 to 48 hours to complete. This is ridiculous that apparently the teams have no direct line of communication. It would have taken a 5 minute conversation with the correct person to sort out the entire mess.
What Now?
So, who do I contact to complain about this? I've had enough of the useless chat & telephone CSO's, and I'm not going to wait 14 days for a response from a letter. Does BT not have a complaints email address?

Answer 1

Why is so hard to complain to BT?
I just went round in circles with a chat representative who categorically refused to put me on to their manager. It states in BT's complaints procedure that:
"We aim to resolve your problem to your complete satisfaction as quickly as possible. If we can't resolve your problem immediately we will agree a course of action with you."
I've now been waiting 3 days to be contacted via the forums mods. I would hope that this has been processed as an "expedite" case, due to the fact that it's been over a month since the original order was made. This is neither quick, nor satisfactory.
I just want to speak to a manger who has the ability to do something. I'm  absolutely fed up of being fobbed off by CSO's. Take a quick look at the chat transcript below if you fancy a lesson in how not to deal with a customer who would like to complain. . .
*Transcript Removed.
The "complaints specialist" CSO above did absolutely nothing to resolve my complaint and then closed the chat session!
This is seriously bad practice ^^ BT's complaints team are not even following their own complaints guidelines.
I really hope that this is an isolated case. If all cases are dealt with such disdain then BT will be suffering a Class Action Lawsuit against them in the near future. I've now wasted such a huge amount of time trying to get this issue sorted satisfactorily and not one single person in BT cares.