Originally Posted by TheBigM:
“No but the DSLAMs powering the ADSL side of things may well do.”
Yes and no. Unless the exchange is located very close to you, most powercuts are unlikely to be widespread enough to affect both you and the exchange, so keeping power available for the router at your end whilst your mains supply is down is likely all you will need (as the powercut is unlikely to affect the exchange as well). If the power does go down at the exchange too, there is nothing you can do about that short of an alternative communications route.
A battery-powered 3G wifi router (such as a MiFi) would be an option provided the local 3G masts nearby still have power, which some of them within range probably will unless it is a really serious power outage covering a significant area (most power outages are quite localised).
A Virgin Media cabled area I'm guessing would be unaffected by a powercut locally, as the phoneline and data services both come together from a nearby box on the street connected to their fibre-optic network, so presumably they have some in-built battery backup to maintain service should the mains supply be unavailable.
Failing either of those, a dial-up modem could always use the analogue phone line which should still work through your exchange if the power is down, for the cost of a local-call for a connection speed of probably around 48kbps maximum. Which is enough for email provided no one has sent large attachments. There are parts of Britain where dial-up is the only option, so it is still in use
The real final option for someone who must always stay connected, satellite internet, is so expensive that I won't say any more about it.