Ok, so I've used that checker to check every single house on my road using the address checker and they're are all served by cabinet 2(including mine oddly enough)
So you've definitely got some kind of records problem - because the data for the property and the phone number don't match up.
I ordered FTTC about 15 months ago, as part of a house move. The line required a survey ... and the surveyor put the wrong cabinet number in. It took 4 months for my ISP to get Openreach to update the records, and get the FTTC order completed successfully.
It needed an ISP willing to put a lot of effort in; a named contact at the ISP so I didn't have to explain the complication again and again; escalation through BTW into Openreach; An openreach engineer assigned a task for a "pair prove" that identified all the connection points in the DP, cabinet and MDF; and a specific team in Leeds to update the equipment database (likely called ROSE).
It also took a procession of Openreach engineers who were tasked with other things (like making a connection in the wrong cabinet) who couldn't do a thing. The pair prove was also done twice - so one occasion didn't trigger an update. Every engineer - from the very first one - could tell the wire went to a different cabinet, and reported this back. But getting the records changed was nigh on impossible!
You need someone very friendly and capable at your ISP - preferably via UK staff, and preferably not first-line phone support staff. Some of the people manning BT's own forum will be in a position to help...
https://community.bt.com/t5/BT-Infinity-Speed-Connec...
Otherwise, you could try asking the Indian support staff to let you talk to someone in the UK, or call one of the numbers that gets you direct to UK staff.
Of course, once someone has checked your records ... and corrected them ... you might still be EO. If that is the case, you could try asking for a copper re-arrangement. That might be expensive, and is best left until you turn out to need to consider it.
Failing all that ... beaming point-to-point wireless across to your parents might be necessary!