If you send me a trust I will give you a mobile number for a BT group CEO. I had massive, massive problems during an office move that they messed up a huge number of times. The only way to get results is to go mental at the people at the top.
It sounds like you have hit the "wayleave" office, the issue is that bt have a tiny wayleave office which doesn't take external calls, wont talk direct to customers and works at a snails pace, this office is the one that deals with any surveys on sites and is an absolute shocker in terms of efficiency.
We did this for business and our office move was delayed by 3 weeks due to bt incompetence.