There's a difference between possible and building a system specifically to help it happen.
This was ten years ago. The task only got easier since then.
On the flip side, the lack of national ID has inconveniences. How do you authenticate yourself when selling your house?
[1] Ethical work. These were needed either after mergers or because of the MS Access syndrome, where every department designed their own customer database.
On the other hand in Poland we do have mandatory ID card, and companies still don't have that much access to your data.
Can't speak for the UK, but I think a lot of the resistance to the idea in Ireland is due to a long history of distrust of the authorities.
Having a ID card does not imply that authorities have right to inspect it at will, or that you are required to carry it with you at all times.
I actually think the other way.
In countries where you have ID card, you just show it to confirm your identity and you're done.
In UK you need to bring your bank statement and utility bills, with your address. Combined with your date of birth, it makes it much easier to match with companies database.