All mobile phones have a special 'emergency' backup.
When your phone tells you your battery is flat it's actually lying to you. All phones save some of the power so that when you dial 999 it activates the power so that it can boost the signal and gives you enough battery time to make that emergency call.
Of course, it won't let you do that if you are in the middle of the arctic - if there are no receivers then there are no receivers (regardless of network). What you need in that circumstance is a satellite phone. But you should be able to do an emergency call in just about all of the mainland UK (some of the more extreme parts of the highlands may be an exception).
So, what I am saying is, that in an emergency (a 'dial 999' emergency) then all phones, regardless of network, keep a reservoir of power to boost your call and give you time to report the emergency.