As Paul mentioned there are a load of variables but;
All of the buildings have large UPS's and generators.
The cabinets that hold the fibre amplifiers are mains fed, usually from the most convenient lamp post or road sign the electricity board can find at the time they provide ntl with the power. Some may have battery and or ups back up dependant generally on who owned the original cable company.
Of course the time they will hold up for varies and is dependant on the usual problems you have with such devices.
The other Amplifiers in the network are fed through the coax network at a lower DC voltage, which (to set folks minds at rest) is isolated within the amplifiers from the coax which connects to peoples homes. In fact customer TVs and videos cause more problems for the network than vice versa. I got many a belt from dodgy VCRs when I used to install
hth