I think you will find they don't have an effective power back up to anything other than the bare minimum of their masts, Im also going to expect they will be in cities especially London
Emergency responders use a separate network so don't have any ability to prioritise their calls over any of the other networks.
I could be wrong in the above and if you have documented evidence to prove the above I would like to have a look. If its based on assumption or Dave down the pub said then maybe have a rethink.
"Storm Arwen (November 2021) was most severe, resulting in millions of customers losing access to mobile and fixed-line connections."
"All affected customers would be unable to call 999/112"
The above statements are taken from
National Risk Register (2023)