I need to move internal BT terminal box, do I contact BT or Plusnet?

[#1]

My "terminal box" ie where the phoneline comes into my house through a hole drilled through the wooden frame of my wooden bay window and I need to move it probably about a foot away. There is no or little slack on the line therefore it will probably need a new cable connection up the wall and across the road to the telegraph pole across the road. The other box is a terminal box which goes back out through the same hole and up to a study/office room on the first floor where my router is connected to the line. My homephone base/answer machine is on the end of the black cable. (see images)
1. Do I contact BT or Plusnet to see how much it will cost and who will arrange for it to be done?
2. Will I have to pay to have it moved (it is in a ridiculous location really but it was there when we moved in and we have put up with it being there for 11 years+). The requirement to move it is a technical one and not because it is an unsightly position)?
3. Roughly how much is it likely to cost?
4. Any other way of moving it? 

[#2]

Can I ask what the technical reason for moving it is ?
Technically, there are two wires that go into the NTE5 box which need connecting up for that socket to work - it's not rocket science to put a small junction box like the one you have there at the moment and extend the cabling but of course that is "illegal" in the eyes of BT .....

[#3]

When I say technical, I meant that it was not just that it looked neater.
I am thinking about having Secondary Double Glazing fitted on this bay window and the glazing unit would have to sit on the face of the frame therefore the boxes, the hole and the connection would have to be probably a few inches away through the (brick) wall.(sorry that one of the images is wrong way up?

[#4]

From a purely hypothetical point of view, I'd suspect the easiest way of doing that would be to disconnect the two wires going into the NTE5, insulate and/or clip off the ends, pull it back through the window frame and drill a hole high enough up the wall to be able to get the cable back through with no splices etc then reconnect the box internally. Obviously the hole would be drilled at a slight downward slope from the inside to out (saves water running back in from outside) and some cable used as a guide would be passed through to help the BT wire find its route inside.
Another option would be to mount theNTE5  box up in the upstairs room and have your modem in there while running an extension into the lower room.

[#5]

Dom, very many thanks.
That seems like an excellent solution to my problem.
I see exactly what you mean and apart from needing a very long drill bit, that sound like well within my capabilities.
Your prompt and very helpful reply is much appreciated.

[#6]

Long drill
I have a few of various sizes and they are very useful.

[#7]

Once again, thanks for the tips but having done a little more research, I may not be able to move the NTE box as I first thought so the question is once again who and how do I contact to get the wire moved/extended/refitted and roughly how much would this cost .
Don't know whether it is BT or BT Openreach or Plusnet who I have to contact.
Help please!!

[#8]

You contact whoever you pay for your telephone line rental.

[#9]

Hi NorthRiding,
You'd need to call our provisioning team - they'll be able to arrange it for you. I don't think it'll be particularly cheap though, if I remember correctly it's around £150 for the first two hours' work though it shouldn't take any longer than that.

[#10]

Thanks very much Matt.
It is a bit expensive and I am a bit annoyed that BT (or whoever fitted the box - some years ago I suspect) put it in such a silly place.
It has always bugged me that they just drilled a hole in the frame of the wooden bay window of a Grade 2 listed building, poked the wire through the hole and screwed the box to the window frame but I understand that if an engineer has to come and sort it, I will have to pay.
Many thanks for the info and help from everyone who has answered. Much appreciated.