Agreed, you are paying for a service, hence the Line Rental which sort of gives it away.
Can you legally move the BT master Box? No you can't!
Well long story short several + years ago, a BT Sub Contractor did a bad job with a re-wire resulting in the wires breaking several years later, so I replaced the whole lot (Master Socket NTE5a, BT80 Box from a BT Engineer) brought the correct spec cable and connected it all up.
There was no way we were going to pay for an engineer callout for something that wasn't our fault.
BT wasn't too happy about it, but what was done was done, but they did some tests and was fine with it, they did say we would be charged if at a later date if it caused damages to their infrastructure, I said fine it won't.
It was easier when we moved over to FTTP due to phone is via FVA and not the copper line, so I just terminated the copper line at the BT80 Box and then once again moved the Master Socket to a new more better location where I then connected the cable the BT Fibre Engineer left in place for me ready for when the FVA goes live.
Once again BT was fine with that too.
But yeah you are not really "allowed" to touch it.