Most mobile base stations have a limited backup battery and some have generators on site. I'd expect telephone infrastructure to have 24-48 hours of backup in the USA and I don't know why Europe would be much different.
Population density is pretty high in many European inner cities. Most of the cell sites around here are on top of apartment buildings and I doubt they have a genset. Here in central BCN the mobile network was completely offline within an hour or two of the power going out.