By "distribution box", I think you mean fibre cabinet.
You can find your exchange name and cabinet number from the BT broadband checker,
https://www.broadbandchecker.btwholesale.com/
You can then find the *approximate* location of the cabinet from
https://www.telecom-tariffs.co.uk/codelook.htm
However, it only knows the *postcode* of the cabinet. The pin it shows on the map is the centre of that postcode, not the exact location of the cabinet. You may need to walk around, either literally or in streetview, to find it.
But in any case, this doesn't help you much. What matters is the length of the line. If the cabinet is only 300m away but the cable is 1km long because it takes a circuitous route, then the speed is limited by that 1km of cable, and there's nothing you can do about it.
https://www.increasebroadbandspeed.co.uk/chart-of-bt...
The broadband checker linked above will also tell you predicted FTTC speeds (based on a mathematical model of the line) and actual measured FTTC speeds.
Plus, when you signed up for FTTC, you should have been told a guaranteed minimum speed. If you are getting that or faster, then you're getting what you paid for; if not, then you can raise a fault.