BT Retail do not provide or maintain the external network. This is done by Openreach who work for all service providers. BT Retail do not get any special treatment.
The standard repair times are shown on this page.
What John meant was that you contact BT to get the phone line fixed.
Once the phone is working again, the broadband should start working again on its own, there is no need to contact BT again.
The service level for residential lines is that if there is a fault, then Openreach will investigate within three working days. If Openreach need to contact you, they will. If they think it's outside yourhome, they will probably just fix it.
If it isn't fixed within three working days, then you can start claiming back your line rental and broadband charges from BT. It's much easier to wait until it's working again, that way you know how much to claim.
If three working days issn't good enough for you, you need to pay extra for faster service. Residential phone and broadband is cheap, and there's a reason why it's cheap compared with a business service.