Just to insert a modicum of sanity into things - as we live in a rural area with no mobile signal we are now without a phone connection once the power is off, which happens quite a lot round here. So BT were meant to ring me today to discuss providing an aux power supply to keep the router live during a power failure - except our power went off so I have no idea if they rang me or not.
This is going to be the big problem as the government want to stop using copper wire for phone lines and change over to voip instead except those that do not have internet access will be left without a phone line. An even bigger problem is the many hundreds of thousands that have the lifeline emergency system that rely on a phone line to work and as you have found out no power means no internet access so no voip phone network.