For the record, I do technically own 3 mobile phones (all 3G I think). One was my mums, the second was my dads and the third was an aunts - I've inherited all 3 in the boxes of junk they left when they passed away. I did try to use them over the weekend to register the NHS QR code (once I'd found suitable chargers), but all 3 have expired sim cards (they haven't been used for several years). It seems that I can probably get a free Vodaphone sim, and a £10 top up voucher from the post office, and re-activate one of them. Register it with the NHS, and then put it in the cupboard. I just need to remember to 'phone my home land line once a month and talk to myself on the answer phone to keep it 'alive' and the £10 credit will probably last a few years. If I can't find the silent mode setting, I'll probably need to open it up and snip the wires to the ringer to avoid being interrupted by incoming junk phone calls.
I wonder what you do if you break down in the middle of nowhere, pouring rain and wife and kids in the car 
Classic whataboutery. Wife and kids? Do you know something about me that I don't? Of course you can construct a scenario where a mobile might assist. But so far, the measures I take mean I've either managed to avoid those scenarios, or found other solutions.
The answer to the question is I'd do exactly the same as I would have done in 1984 when I first started driving, and mobile 'phones weren't a thing. Since then I've been stuck in a paddy field in Japan, an irrigation ditch in Arizona, and up a muddy track in Hungary. All three were 'solo' and due to my own stupidity, but I'm still here to tell the tale. Darwinism hasn't got me. Yet.

Anyhoo, back to the QR thingy... You assume that the global apps don't communicate data with the various THEMs on the basis that they tell you they don't...
The QR code only proves you've been double jabbed. If 'they' really want to find out who you are, the NHS QR codes are fairly useless. They'd want Photo ID - which means passport.
I know - 100% - that the QR code scanners don't connect with the NHS system. The scanners work on airplane mode, and on systems with the WIFI/3G/4G disabled. The scanners also work in places with no signal - like up mountains. The QR codes contain a sort of digital certificate, similar to those used for signing Windows kernel mode drivers. The security/encryption codes embedded in the QR code ensure that the 'payload' has not been tampered with, and therefore the names and dates etc are valid. Sure a security/border/government agency could then check your records for whatever, but there is no system in place to access NHS records in real time. If there were we wouldn't need NHS QR codes at all because those records could be directly accessed from passport info.