More than likely the phone issue is the cause of the broadband problem yes. A loop issue sounds most likely here. First move would be to check the phone tester-but it looks like the site is down at the minute.
So in that case I'd start with the internal checks-disconnect everything and remove the front plate of your BT socket-dont do this if you have one of the old plain white sockets without a split across the middle-then plug the phone on its own into the test socket behind. Does that work? If yes, something inside is causing the fault, and you'll want to build back up piece by piece until you lose the phone line again to find the offending item.
If it doesn't work on its own, try a different phone if you can. If that then works-the phone handset is the problem. If not, you have a line fault which you'll need to report either by calling technical, or through the website when it's back up.
