Drop in the Ocean
Overhauling emergency commo systems is just one small part of issues that the UK has in relation to Emergency Preparedness and Response.
I work in Emergency Management and the UK really needs to get off its ass in that regard, especially with the Government worrying about the effects of climate change on natural disasters yet making absolutely no public planning as to how to deal with it. There's nothing like NIMS, there's an old version of ICS that the Met Police and I believe City of London use, The UK's idea of Comprehenisve Emergency Management is not fit for purpose if you ask me, which is a shame as your Civil Defense plans were among the best, much better than the halfassed shit that FCDA and OEP had in the US at the time until FEMA was created in 1979 to unify it. Its a shame that Thatcher, Major and Blair all decided to virtually ignore domestic emergency planning aside from anti-terrorism, the UK could still be setting the standard, and your standards and doctrines from what I've seen (some are still classified) were a fuck of alot better than California's and the Federal Civil Defense Administration's plans, which is what the whole US used and still uses in some forms such as the Incident Command System which came from CALFIRE in the 1970's, though was not adopted as a national policy until 2004. Also, Counter-Terrorism isn't even emergency management, its a Policing, Intelligence, and Military function. Emergency Management deals with what happens after a gas line explodes or a terrorist blows it up and takes out a council estate or a tube station or what have you. But if you're not preparing or mitigating, and have a codified means of preparation and mitigation what's the point of reponse and recovery?
Your Government doesn't even have a standing agency under the Home Office or at Cabinet Level (where it should be) to assist the Prime Minister to handle it, and COBRA hardly counts. COBRA, from my understanding, is basically a half-assed version of our National Watch Center in DC and a non-survivable version of the Mount Weather Special Facility or Raven Rock's C4I centers. All it does is provide a means of the Cabinet Level and executive (in your case the Prime Minister) to assess what's going on and manage from the top, which doesn't work too well. CALFIRE realized this in the 60's when they created the common Incident Command System where the Incident Commander is the most competent person.
What the UK needs is a custom version of NIMS geared toward the UK's hazards. I see stories about the floods and storms every year and people dying from them and the response being somewhat piecemeal and patchwork with noone in overall control on a permanent basis, and none of the responders on the same page. Perhaps adding an extra layer of bureaucracy like a UK style FEMA is a dumb idea, but a framework of incident command and control for the existing agencies to use is a good idea and a UNISDR best practice. If the Developing World can do it (and does do it, the Ebola outbreak's a good example though it has some flaws and heavy handedness from some nations Armed Forces) there is no reason that a common incident management system should not be implemented.
Anyway, on to the subject after the Hurricanes that The Man Who Fell to Earth mentioned, the Cellular systems worked as they were supposed to as long as the base stations survive somewhat. To a user they'd appear to be down and unusable, but to the operator and the government as well as some FOUO (For Official Use Only) users it works normally for voice for the most part unless its LTE and works completely normally. Without LTE you don't usually have a data channel to speak of unless you can con the National Guard into using a Military SATCOM, they don't have to let you use it but you do have voice, and voice is good enough to compile an ICS-209, the datasheet we use for tracking who is doing what and where. The Incident Commanders at the Federal Response Center and National Watch Center engaged the US' equivalent to the MTPAS, but with our systems, we can and do lock out anyone who isn't on a SIM, landline or IMEI which is enabled to use the National Communications System from using most networks. Notably, the TCP/IP, X.25 and Frame Relay networks aren't subject to it aside from some traffic shaping to allow FEMA's teleregistration system and the Air Force's Air Material Command, Army Surface Distribution and Deployment Command, the Military Sealift Command and USTRANSCOM, as well as the Postal Service (yes, the Postal Service, I'm not joking. It sounds weird but there's a major reason for it when we're accounting for the deceased and missing that the NDMS may have missed at DMORT)