New BT Master socket

[Alrock]

Hi...
Need advice on getting a new BT Master socket installed in a new location.

Currently my phone line comes out of a gray box on the wall outside of my living room. The line then runs out of this box, up the side of the house & through the wall into a bedroom at the far end of the house into a socket (installed I believe when the bedroom was being used as an office with a fax machine connected). It then runs through another cable (spliced back together after accidentally getting cut) that snakes it way through the house to another socket in the living room (via a socked on the stairs where the original phone was) which my phone & router are plugged in to.

My question is how would I go about getting a new master socket installed in the living room connected directly to the gray box outside through the wall so that I can rip out the maze of wiring that seems to run everywhere (There is also another old line coming into the house in the downstairs toilet (the original phone line I believe), the one I assumed was the one connected into the living room socket (quite logically since there was also an extention plugged into the stairs socket running to the bedroom) hence the accidental cutting of the other cable)?

More importantly would it be a worthwhile exercise?
Would it improve my internet speed?
What if I upgraded ny internet to FTTC would that make any difference?

Thanks in advance for any insight you might be able to provide.