A lot of things end up being tied to your ID number, and it becomes very difficult to limit the collaboration of companies to create a dataset about you, never mind making it easier for the Government to track people en masse.
Lack of ID card doesn't stop UK to share all your data with private companies, like in case of care.data and now also HMRC data. I never felt as tracked as in UK, where all companies know where I live and lived for last several yers.
On the other hand in Poland we do have mandatory ID card, and companies still don't have that much access to your data.
I'll have to break it to you then: it's exceedingly easy to get the same use of data without an ID. The lack of national ID does not protect your privacy.
The feeling of protection hinges on how easy it is. A bit over ten years ago I was working in database "cleaning": merging databases from different organizations[1] into one coherent dataset. The data volumes were large, but other than that it is a simple task with low error rates and one which absolutely does not need global unique IDs.
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.
Definitely the same in the UK. It's likely the death of Blair/Brown's <s>citizen tracking</s>ID card scheme killed the idea for other countries considering one.
Case in point: HMRC (UK Taxman) is about to sell 'anonymized' taxpayer data. With enough 'anonymized' data-dumps and CPU power, at some point, it will become trivial to correlate an ID Card ID with datapoints.
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.
Same issue as with SSN in the USA. Lots of things requesting it what should not ever have access to it, opening people up to everything from privacy intrusion to identity fraud.
I wear a tinfoil hat because governments have a history of abusing their powers. Although we live in steady and somewhat well-governed democracies, there's no guarantee that this will always be the case.