To your last point: isn't it sort-of dangerous to rely on a TV news channel in case of serious events? Power to households may be off; people may not realize that they need to turn on their TV set.
Something like a network of alarm sirens that can also speak would be more resilient. We have such a system in Prague. Every 1st Wednesday of each month at noon, it is shortly tested. If Prague can afford it, most of the UK could surely as well.
The key is multi-modal communication. People may not have a standalone radio in a home any more these days, but they may have a TV set.
Basically, the initial warning via sirens, firefighter trucks or Cell Broadcast tells the people to find one of the four networks (tv, radio, internet on a PC, internet on a smartphone) and inform themselves what to do.
The more avenues the authorities have to distribute both the initial warning and the followup information, the better.
Something like a network of alarm sirens that can also speak would be more resilient. We have such a system in Prague. Every 1st Wednesday of each month at noon, it is shortly tested. If Prague can afford it, most of the UK could surely as well.