Your issue has nothing to do with BT , no more than (for example) Sky or Vodafone, so the BT Mod is unlikely to offer assistance, you are not a BT customer, and ultimately you may chose to use a competitor anyway .
If your address didn’t exist when the area was surveyed for FTTP (and that could have been years ago ) then clearly no provision could have been made for a non existent property , you say the FTTP physical infrastructure is right outside, is this telegraph poles or underground service , if underground did you supply Openreach duct from your property wall to the curtilage ?
Fill in this formwize , the ‘my neighbours can get FTTP but I can’t’ is the pertinent section , that should prompt OR to look at this and get back to you , if FTTP is overhead from a pole and you are within span range (and no problems with achieving height for the wire , so not a bungalow for example ) , then service may relatively be quick and easy , if duct is needed then depending on the exact requirements you may need to contribute towards costs .
https://www.openreach.com/forms/fibre-broadband-availability---customer-form
