Sounds like the school have an FTTP connection, not an FTTC connection if they have a direct fibre feed.
It's all very confusing with BT claiming they have a "fibre" service in your area, when it fact it's just glofied DSL with a shorter cable length, and thus a faster speed (speed of DSL is reliant on many factors, one of which is how long the wire is from your exchange to your house). It irks me when they bang on about fibre broadband in their ads.
They've just moved the DSL hardware (which used to be in the exchange) closer to your house. The last mile (so to speak) is still shÃte copper wiring that has been in service for decades.
The long and short of it is that BT are unlikely to get infinity speeds to your area as it is rural. If you don't have any cabinets in your are, they are either well hidden or in pits, or perhaps you have an exchange only line, ie. where the line is wired directly back to the exchange and not to a cabinet.
To be clear, BT do not claim to have a 'fibre' service in my area. My phone line goes back directly to the exchange via the underground chamber. The connection speed is 8MBps, and is profile limited to 7Mbps. I'm generally happy with this speed as it gives me all I want.
In fact at the moment there is a fault with my ADSL service and BT are trying to sort it out (hence my gentle interest in this thread). It's amazing what those engineers can tell you about the performance of your telephone circuit minute by minute so it seems and going back a few weeks.