BT Retail has a minimum speed (15Mbps?) for their Infinity product line. Below that speed, they won't sell you a product with the brand name of Infinity.
However, they have an alternative brand name that they *will* offer you instead. In technical terms, it uses the identical FTTC setup that you see in the checker, so doesn't represent any other form of fibre. BT Retail are prepared to offer you this product line.
Most ISPs do not distinguish, and would offer you their FTTC product regardless.
Because of your distance from the cabinet, and the low speed that the FTTC upgrade has brought, you still qualify for some future upgrade via Superfast Essex. That could be FTTP, or could be a closer FTTC solution (AIO, FTTrn, or whole new PCP/FTTC pair). Or you (and nearby houses) might be too expensive for an extra upgrade, and you get left off entirely. However, BT Retail will not start offering any of those options until they have been installed and gone RFS (ready for service).