Looks like two separate BT lines.
The one near the telewest socket is a newer BT master socket.
The second socket...
This one is also a master but take note that it does not have BT or a T written on it indicating it might be something someone bought on eBay and did a DIY job.
The wiring coming out of the faceplate is very concerning and the exposed cable we see looks dogey.
Anything installed by BT would clearly be labelled.
It does not look like a telewest socket either.
It could be an extension from the socket by the telewest socket and somebody dogey changed it to another master but that would be very bad.
It might also be a second line (hopefully)
The socket in the garage is not a master so do not locate the broadband here that's a bad idea.
The best we can hope for is that the BT socket near the telewest socket is activated and the second master does not go live. Then locate your modem etc here and it should perform well.
If both masters go live someone has really played around with the wiring quite badly...