Yes, BT Infinity is FTTC (Fibre To The Cabinet).
Broadband speed is, roughly, inversely proportional to the length of the copper between your router and the DSLAM (that magic box that converts the signals over the copper into network magic). The longer the length of copper between you and the DSLAM the slower your broadband is.
Originally your 'phone line is is a piece of copper that runs from your house to a nearby cabinet somewhere and then, along with lots of other people's bits of copper, all the way to the exchange.
When DSL was first rolled out the DSLAMs were located at the exchange, so if didn't matter if you were only 100 yards from your cabinet, it was still 6km in total to the exchange.
With FTTC they build a new, slightly larger, cabinet near the existing one and put the equivalent of the DSLAMs in the cabinet. Now the run of copper to the DSLAM is (for this example) only 100 yards, and that allows them to use VDSL2/etc to get speeds up near 80Mbps (if you're really close). The cabinet is then connected to the exchange using fibre optic cable so that capacity/speed is not an issue.
If your cabinet is miles away you may still get a speed increase if FTTC decreases the total copper run length by a large margin.
Of course, if the cabinet only serves a small number of people then it'll be way down the list of priorities for OpenReach to upgrade to FTTC as the cost per subscriber is going to be much more (laying fibre between exchange and cabinet(s)). It also depends on whether your exchange has had the equipment upgrade to handle FTTC as the exchange now needs to handle the incoming fibre.