Interesting update for you all.
I ended up going another few rounds with BT - someone put me through to a BT broadband tech support person who very helpfully look at things, my neighbour's line, and said there should be no reason I couldn't get a FTTC service. My hopes raised, I went back and tried to order again.
Finally, exasperated talking to the last useless BT parrot claiming I couldn't have it because the system wouldn't let me order it (she didn't even seem to know the difference between old style ADSL, ADSL2 (which I could order in 2012), and the two FTTC services (Infinity and Faster Total Broadband), I asked her to be put through to her manager... where she dropped the call.
So I filed a written complaint.
2 days later someone phoned me to say he was looking into my complaint, but I've heard nothing since.
BUT 2 days after that, magically BT's website allowed me to place an order online for Faster Total Broadband saying I could get 3Mbit. Installation was Wednesday.
Engineer said his tester wouldn't sync, but he plugged the vdsl modem in anyway and it did sync. Ran a few download tests, looked good. Declared victory and I've had 15Mbit down 1Mbit up since then
BT Broadband: 512kbps