When it comes down to it .. assuming you don't have cable and you are not in Kingston-u-Hull you will be using BT to provide a copper wire between you & the exchange. You pay rental to BT for that line. You can buy an internet service from anybody who takes part in local loop unbundling in your area and will provide an ISP serive over BT's wires.
You can buy a bare bone BT services and stay with your Web hosting compnay .... or Google about and find someoneelse.
The difficulties arise when there are faults ... BT will test line and line only ... if they are providing broadband service then BT will take next step and resolve issues .... if your IS is not BT you can end up in a lack of ownership - each saying their part is fine.
I have BT business Braodband and have had this since the day it became avaialble .... it is reliable, and good value for money ..... I would prefr SDSL, but not an option at present.
So the answer is chose who you want ... if price difference is not great, then BT is worthwhile ... if big saving, use an alternative ISP ... and accept service could be an issue if it is needed - for non-business use, may be acceptable to you.