As CMDR Heisenburg said, I'm not worried about the computer system, or backups or any of that.
I'm wondering about how you can continue to.run the NHS (albeit at reduced efficiency) with no computers.
Stuff like having printed copies of the phone directory, a system for registering people with simplified (pre printed forms) starting rotoas already drawn up for drawing extra.staff (particularly admin, porters etc) to help with moving the paper and files.around.
Even simple stuff like having those rope barriers and mowing where they are laid out to control the extra queuing to prevent corridors being blocked, enough trollies.for moving stuff about and so on.
It's about graceful failure not catastrophic collapse.
Generally speaking you can't, you'll have to go back to practices that meant a certain percentage of the patients die, just as they used to. You could look at this as bad or see the benefit in modern information/computer tech.
I have very little say in these things, but here's an idea.
Each department that is considered essential has a private, hard wired, not connected to any external network, server (and clients for that matter). This network can be linked between departments but can not be accessed outside this local wired network (it's not connected to the normal local network let alone N3).
Given a disaster such as this recoveries from the most recent backup of the main system can be placed onto the segregated network. This would allow a local hospital to continue on its own pretty much unaffected. It'd need transaction logging for all that happens on this system to be placed onto the actual live systems once the threat is over.
The trouble is there may be vital, life and death, information at one site that's needed for that patient to remain alive when transferred to another so you'd also need a way of transferring data from one locality to the other. This could be a phone call or encrypted USB stick or other but it's possible.
It's about the only way I can see such a complex service truly having Business Continuity to a degree that it can still function without massive delays.
The cost though. Right now there's no way the NHS could afford this. You're talking duplicated servers, PC's, network cabling, network infrastructure, OS licenses (client and server), system licenses for additional server software that can run into millions for each site. All this would have to be upgraded manually to maintain the viability of those servers/PC's/networking/software/printers/smart card readers and so on so you'd need extra staff as well.
Like I said you can do this if you allow for redundancy and we can, as a society, decide that's worth doing. It'd be a tiny increase in National Insurance but it'd make a far more redundant system.
Of course the one off deal with MS that Jeremy cancelled would help massively with mitigating some of these costs - but hey if you see him in game feel free to waste him - I know I have.