I have four old smartphones, but I hope this alert only goes to the one with a sim in it, otherwise it's going to be a bugger for me.
I was just thinking about that, and the claim that it does work when the phone is switched off.
I can see it working without a SIM, because some phones can still be used for emergency calls without a SIM, afaik.
(Edit: i think it will be limited to phones with an active UK SIM. Mostly because they said it works even if you are abroad. That means they must sens it to phones based on their SIM, and not their location. They might miss a few people that way, for example those that use their phone without a SIM just over wifi.)
I can less see how it'd work when the phone is switched off. For example, if it has run out of battery, I can't see how it'd work. Maybe some phones can be woken up remotely? But they'd still need battery for that to work.