"One of the rights we've grown used to in the UK is not being challenged for our "papers". "
Doesn't seem to be the case these days.
There's a massive kneejerk reaction to ID cards, and perhaps to the police being able to force you to identify yourself (which they can in a quite a large variety of circumstances, just not at will) but you absolutely get asked for your ID by the UK cops.
If you're a citizen who has never lived outside the country, then it's almost invisible, since mostly it's about proving your legal right to be here. But the people being hit by the Windrush scandal have had situations where they've been asked "papers please" and being unable to provide them, lost their jobs, rentals and access to healthcare.
So no ID card, no papers from the Home Office until you can prove your residency (auto reject unless 100% complete), but you'll need those papers.
Don't worry citizen. Your rights will always be protected.