The top paragraph referred to UK internal flights.
Yet you persist with posting about ROI.
In my neck of the woods, domestic flights are like hens' teeth, but Flybe make it quite clear what identification is required before they will allow you to board one such and they all require a photographic ID other than the one exception of a pension book.
Only a few of those IDs give indication of citizenship or permission to be in the UK.
This will be for security r/e someone blowing the plane up, and not an immigration requirement I presume?
Incorrect. It's for revenue prevention. The x-ray and metal detector is for security.
ID is not required, but as the website states [Photo ID] may be requested at certain points in your journey.
You do not have the 'right' to not be indentified by the authorities just because you're on a domestic flight.
No, we live in a free country. The authorities have the right to verify your identity for the purposes of terrorism, not for immigration purposes.