Estonia's system was an area of some fascination for me years ago, so here's what I can remember:
After splitting from the Soviet Union, Estonia were basically starting from scratch with their telecoms system. Finland offered them their old stock to get started, but the Estonians decided to instead treat it as a greenfield project and deploy the most modern infrastructure available at the time. Compare to the UK, where most of our infrastructure is literally crumbling as it passes its 50-year predicted lifespan and we spent almost a decade of time and tens of billions of pounds on a vapourware railway line. So the technical inheritance (or lack thereof) favoured Estonia.
I don't know much about how the Estonian system was initially built, but I would imagine a post-Soviet state likely retained enough state capacity to do it mostly in-house (and perhaps they received outside funding too, as the '90s were a period of largesse). Compare to the UK, where state capacity is effectively nil and the project would invariably be outsourced to the same contractors and consulting firms that have taken on every other aspect of government, with concomitant price and time overruns (see also: train).
A crucial element of the Estonian system is that data is private by default (see https://e-estonia.com/solutions/e-governance/e-services-regi... ) If I recall correctly, any government agency can request access to specified data for a state purpose, but each request must be reviewed and approved by the data subject. All access requests are logged so a subject can audit who has been accessing what (which suggests maybe it's possible to bulk approve access in advance, or grant persistent rights to someone like one's own doctor). In comparison, the Snoopers' Charter granted unfettered access to Brits' Internet connection records to a huge number of agencies, from the security services to the Food & Agriculture Agency (see https://en.wikipedia.org/wiki/Investigatory_Powers_Act_2016#... ).
Estonia is also recognised as a global leader in IT security, following massive investment after Russia-attributed cyberattacks in 2007; they host the NATO Centre of Excellence and the eu-LISA HQ. As far as keeping one's data away from prying outside eyes, they're probably a pretty safe bet. As for the UK… (Eyes passim ad nauseam).
Lastly, I believe Estonians generally report greater levels of trust in their government than Brits. 2023 figures suggest the gap may have narrowed from when I last looked (I can't say I've been following Estonian politics, so I couldn't suggest why) but still some 37.8% of Estonians say they trust their national government as compared to 26.7% of Brits (see https://www.cso.ie/en/releasesandpublications/ep/p-trsic/tru... ). And there are certain sizeable constituencies in the UK where, in light of historic abuses, they are even less likely to ever trust the government: Scousers; northerners; women & ethnic minorities (specifically for the police, doubly specifically for the Met); environmental activists (see the spycops scandal); and people of Irish descent. I'm sure there's some skeletons in the Estonian government's closets, but there's a limit to how much damage you can do when your state is 35 years old rather than a centuries-old former world-spanning imperial hegemon.
Those stated trust figures also predate the UK government's support for the genocide in Gaza, which has doubtless had a significant impact on that figure; even people who wouldn't have considered themselves particularly political a couple years earlier are appalled at the regular arrests of protesting pensioners outside Parliament (see https://www.theguardian.com/world/2025/aug/09/palestine-acti... ). The incredibly unpopular incumbent government is only the latest in a long line of increasingly authoritarian regimes of both the political right and (allegedly) left (see https://www.hrw.org/news/2024/07/09/labour-needs-arrest-uks-... ), meaning everybody in the country of any political persuasion can think of recent examples of why they might not want to invite increased government surveillance. Plus, with the recent passage of the Online Safety Act, most people are now primed to associate a new digital ID with the government wanting to know their porn habits, and we're a famously prudish nation.
So, in short:
· the Estonian government had the ideal circumstances, made all the right choices, prioritised privacy and security and are reasonably trusted by their citizens
· the UK government has doddery old infrastructure to work with, no money left, an addiction to outsourcing in spite of repeat disasters, a track record of authoritarian disregard for privacy and have little to no legitimacy amongst the populace
And, as others have pointed out, there's just no obvious constituency in the country that would be interested in this sort of thing (outside of Tony Blair and his mates) and no obvious problems that it provides a solution for; it seems like a hard sell, whether on ideological or practical grounds.