A few general observations and suggestions...
Most European Countries have an ID card and/or population register
This is because they have land borders which are easy to cross, by contrast we have relied on port control. How good this was is debatable and certainly it doesnt seem to work well now.
Then there is the Spike Milligan case, born to Irish parents at the time when the UK was under British rule and who was in the British Army in WW2 but told when he applied for a passport 'No'
We also have all the issues around 'Windrush' and of course successive Governments have imposed increasingly complex rules on landlords and employers requiring them to check the bona fides of their employees and tenants as well as a requirement to provide ID to vote.
Given that about 75% of the UK population possess a passport I would suggest that rolling out an ID card over - say a 10 year period would not be particularly difficult. It could also be issued when people claim Universal Credit because lots of ID Documentation is required for that.
As part of the roll out I propose that those legally in the UK shoud have the option of applying for UK Citizenship at no cost
I would also suggest that people born before a certain date would not be required to have an ID card but would be issued with one of they applied for a passport.