When we moved here, the FTTC order needed a survey before being properly accepted. Within 48 hours records had been created for the property, confirming FTTC available from the cabinet 20m away.
Unfortunately, when the appointment happened, it turned out the survey was wrong, and the property was actually connected to a different cab 100m away. While they could get the phone working via a link at the exchange, the FTTC order would never work, with a port allocated in the wrong DSLAM.
It took 4 months to sort out, with a lot of cooperation from my ISP, though even that required me to bypass normal customer services to get a single named contact on their online forum.
The key task that an engineer was tasked with, eventually, was a "pair prove", where he had to confirm exactly which pairs were used in the D-side and E-side caves, and what joints were in the DP, PCP and MDF. That then needed an update in the Openreach back-end system (ROSE?), which then flushed through to the online system a few days later.
In one sense, I was lucky, because the ISP would at least accept an order, and then be forced to help.
Your first point to get things done is via your ISP support staff. If that goes nowhere, use the emails to the bosses of BT - the CEO of BT group, the CEO of Openreach, and the Chairman of BT.
I didn't get help from the two CEO's myself, but others have. Some have found contacting the chairman's office to be most useful.
My case didn't have a new AIO being added - it was two separate standalone PCPs.
BTW - A live to live migration is one where a customer that had a fibre connection on the old cabinet gets migrated onto the DSLAM on the new cabinet. All these lines must be migrated first, before any new orders can be accepted.