Somewhat perplexed about MNs interest in emergency planning. 
My main job is not emergency planning but I would have a role in certain national emergencies. I would be a small cog in a very large wheel, but have a general awareness of what goes on. I would be part of sampling teams providing information about releases of hazardous materials.
However, what I do is very specialist and there are literally only a few hundred people in the entire UK that do what I do so forgive me if I don't go into specifics as I don't want to out myself.
In high profile national emergencies (eg. terrorism, Buncefield fire) everthing is controlled by the Cabinet Office Briefing Room (COBR) and the Agency I work for provides information that helps direct strategy. Many other Agencies etc are involved.
I have already said that there is no Zombie Plan. I would expect that it would be treated like a very extreme riot and the army and police would be involved.
Local councils still do have emergency planning departments and would deal with looking after any evacuated people in sports centres etc.
Companies that run sites where an accident may cause an off site hazard are required to do what they can to prevent such emergencies, but also have plans in place to deal with them, that must be rehearsed. There is a lot of work that goes into preventing emergencies and also a programme of rehearsing possible accidents (chemical or nuclear release) that involve the companies themselves, along with the emergency services, public health, regulators etc.
HTH