It's kind of complicated in the UK - parts of both the left and right have issues. Some reasonable, some less so, etc
Around the same time of the original proposal for National ID, the government lost discs containing the data (including NI numbers and even bank account details) of 25m people, 7.25m familes. They were literally lost in the post. Understandably this made a lot of people sceptical about 'the government's ability to protect it's data'
It was already an unpopular idea. A lot of this was kind of libertarian-y people, combined and heightened by a post-WWII fear of having to carry 'papers' and present them for identification. How reasonable this fear is/was is up for debate, but for better or worse it was a big part of the conversation.
Then in the years since there's been more concerns raised: things like the Windrush Scandal. In case you're unaware, basically a lot of immigrants from the Caribbean who had been here for decades, sometimes nearly their whole lives, and who thought they were Citizens, were apparently not. There were pensioners who lived here since they were kids and who followed all the correct procedures getting deported to places they had never meaningfully lived in.
Some people say that a National ID would have prevented this - but others say that since the UK is apparently so inept at dealing with this data, it's just more evidence that we could end up in a system whereby if you can't get a card for whatever reason, you could face discrimination or even prosecution.
So yeah I guess it basically comes down to a distrust of the government combined with a British Libertarian mythos
For what its worth, personally I don't think a National ID inherently poses any problems that don't already exist between documentation and our data being collected online etc. But I'll admit that on a gut level I don't like the idea, even if that's a bit irrational
https://www.ft.com/content/2ec95b9a-4709-11e8-8c77-ff51caedcde6
https://www.theguardian.com/politics/2007/nov/21/immigrationpolicy.economy3
