Bremen your reply sounds very useful, if only I knew what any of that stuff means haha. I will google everything one by one

Thanks!
The BT VDSL faceplate has a set of terminals inside where you can connect an extension to the data socket. It allows extension wiring without anything plugged into the front of the socket. They're IDC terminals where you can push in solid core wires and a set of blades cut through the cable insulation and into the copper. There are proper tools for this (Google 'Krone') but for a one off you can get away without.
The IDC socket requires solid core cable. Cat5e and CW1308 are just cable standards. For what you're doing CW1308 should be okay and is easier to find in white and in sensible lengths. It's also thinner and more flexible that Cat5e.
I'd use Cat5e because (1) I have it available, and (2) it can also be used for data at a later date.
Whether you use Cat5e or CW1308 you only need to connect a single pair. By convention this would be the blue pair but it doesn't matter.
At the remote end you can either crimp on a plug which is fiddly and requires special tools, or terminate at a faceplate.
For the faceplate you just need a standard Cat5e Ethernet socket which are easily available. You terminate your cable pair to pins 4&5 in exactly the same way as you did at the master socket.
You can then plug your modem/router's RJ11 cable into the extension socket.
You're best bet is to Google 'VDSL data extension kit' or similar and you'll find sellers that'll provide all of the required parts and the necessary instructions. It shouldn't cost you much over £25. Just make sure that they specify the cable is Cat5e or CW1308.