As tolien said, yes, they are seperate.
I've recently made the same change myself. I was an NTL customer for years then moved to a non cabled area, so now i've got BT and Pipex.
You will need to contact BT first to get a line installed and/or connected. Once you have a working line, just visit the Pipex (or whoever) website to sign-up. The rest will be done by Pipex, including arranging for BT to install the ADSL line for you. Was all straight forward for me.