Contention and crosstalk are very different. The former can be solved by an ISP willing to throw money at it, but crosstalk is a physical/electrical limitation of the wiring twist cabinet and customer premises.
FTTC is Fibre to the cabinet.
If testing at master socket one thing is commonly misunderstood, especially by Indian helpdesks... you need to unscrew the faceplate and pull it, to reveal the 'true' master socket. That eliminates rest of the internal wiring. Simply plugging the modem into the master socket faceplate, vs any connected extension, is unlikely to make any difference.
250k is very slow. You don't say whether that is byte or bits but either way, it is slow for FTTC. Roughly how far are you from the cabinet?
alternatively, who's your ISP? Some do apply 'traffic shaping' policies.
PS, just reallised, you already said BT.