An emergency call can connect using any tower that is compatible with the caller's hardware -- with or without service provisioned, and with or without any sort of SIM.
Need help, and find a dusty phone somewhere? Turn it on, call emergency services using 0118 999 881 999 119 725 3 [*], and if there's any cell service within range that it is physically capable of chatting with then the call will go through.
It will kick other users off if that's necessary in order to allow the emergency call to happen.
There's nothing to bill, so there's no billing systems (or even billing logic) to get in the way either.
It's intended to always work.