Had that problem here too, I live in the country, storm Arwen came, the power went and so did the mobile broadband and mobile phone signals. I have backup power so everything at home kept working.The mobile broadband and mobile phone signals come from different providers and different masts but both went down as soon as the power went off.
Our power was off for nearly a fortnight although the mobile signals returned after a few days as power was restored to the masts (phone first and a few days later, the mobile broadband). Looks like there's no UPS supplies installed at the masts at all.
The thing that surprised me was the landline phones went off when the power failed too despite still using POTS, however, the exchange now has fibre to the rest of the system so I suspect the POTS (analogue) part in the exchange was still up but no digital backhaul because the fibre to the exchange was down but that's only a guess. It did come back after a few days although it was nearly a fortnight before power was restored to the houses here due to the extent of the damage caused by Arwin.
There was a bit of an emergency involving an elderly resident, his alarm didn't work because his landline was down, one of the neighbours drove to get help -- in the old days the landlines stayed up during power cuts, now it seems nothing does.
The mobile systems work well as long as there's no power cuts but out here in the sticks power cuts are quite common in stormy weather.