Is it possible to have a whole new BT line installed?

[#1]

Hi All, I've been having a long running battle with my broadband and have had BT out in the past to look at it. The problem appears to be a very poor quality line. My question is would it be possible to have a whole new BT line run from the green cabinet In the road to the house? My master socket is in my lounge, so the line must run under the floor to the grey box on the outside of the house Wall about 8m away. The line from the grey box on the house to the green cabinet must run underground about 100m as there are no overhead phone lines. I'm absolutely desperate to resolve this and might be prepared to pay BT to run a new line if that might help me. Does anyone have any experience of this type of thing? Thanks and best regards, Simon

[#2]

Sorry I should also mention that I live down a private road and the neighbours would not appreciate me asking BT to dig up the road, so can BT pull a new cable through? I saw Virgin Media do this recently for a neighbour. Thanks, Simon

[#3]

Generally, not unless you paid for it.
You could pay for a completely new telephone installation, put broadband on top, refer yourself for both services and close down your initial account.
Might even make a profit in the long run

[#4]

OMG! 
Question - has the cable from the Grey box to the Master been tested seperately (and properly)? What are the colours of the wires in this cable (and the colour of its sheath)?
As far as a pull through of a new cable goes, that would depend on whether the existing one has been correctly installed in ducting/conduit. In any event, if you asked for an additional line they'd probably try and use a /the spare pair in the existing cable unless you were quite explicit about a new cable - could be a very pricey job!
I'd have bit of an investigation from where the u/g cable from your grey box goes before contemplating what to do next.

[#5]

I had 2 lines installed  BT used the spare wires on the in coming cable, so he did not need to run anymore cabling,
check to see if your incoming line has 2 or 4 or 6 core cabling first
Puddy