I think there's one thing perhaps worth clarifying.
Your contract is with BT Retail, and they have *sole* responsibility for fixing this problem. It doesn't matter whether the issue is within their own systems, or within external systems they talk to - both the diagnosis *and* the resolution is entirely up to BTR.
I wouldn't bother trying to suggest possible problems and solutions to them. Unless you have intimate knowledge of BTR's systems (e.g. you used to work for them), it's not going to help. What is required is simply for the problem to be escalated within BTR, to a suitable person who understands the order management systems and can fix the problem.
The problem description is clear and unambiguous: you ordered a regrade to a 150M service, you are still on an 80M service. Therefore, the order has not been delivered.
If this isn't happening, then in the first instance you should ask for evidence that the problem has been escalated internally. If still nothing happens, then raising an official complaint with BTR is next step. After that, there's the OFCOM dispute resolution process. Optionally you can call them out in public on twitter or raise it directly with the CEO's office.
(Of course, the one group you *shouldn't* call out is Openreach. The problem may or may not be in OR's systems; but even if it is, it's entirely BTR's responsibility to resolve it with them)
Don't forget your option option, which is to walk from BTR and choose a more reputable service provider. When you are dealing with the complaints team, if they can't sort the problem then at least they should be able to release you from your contract. And if you've chosen BTR because they're the cheapest, well, now you know why