I've just moved house and had a 'false green' from the BT checkers too. Yes, my line is connected to an FTTC enabled exchange only 4.5km away - I should get some service. But. The cable was installed by a drunk and is actually 7.5km away. I can't get FTTC but can get ADSL. All 980k downstream of it. Luxury.
There is another cabinet 2km away (i drove to check the distance myself) but there is no way BT or Openreach will move the line from one cab to another. BT simply state I'd need to talk to Openreach, who eventually (through the use of a few sacrifices chickens and a ouija board to actually get in touch with them) said 'hmmm, yeah I see the problem. We don't do things like that. It's just the way it is.' Not even a 'sorry' appended to the statement.
£4m released for poor internet connected sites, but not me it appears. I had the quiet word (and I'm not naming names but it was a BT employee) that there would need to be benefit to more than one property for any consideration for enhancing the service. As there are 3 houses in the entire postcode I can't see we qualify.
Yes I have a satellite service too. Ridiculously expensive, doesn't work often in winter, latency so slow I get to watch youtube as a series of 4 second clips and it is still only 20Mb down - allegedly. Oh, and I'm limited to 10Gb down per month. That's software updates taken care of then...