Why don’t we choose to do it once, well, rather than multiple times on a shoestring?
1) There's no such thing as a government IT system that works well - and no hope of ever having one.
2) All the organisations (and the rest) have different requirements and priorities, sometimes mutually exclusive - both internally and with each other.
3) Such a database would be prone to abuse. Why should some PFY at the council (say) get to see or change your passport data?
4) A database like that would be a remarkably bad SPoF.
5) The database would be an Orwellian nightmare far beyond anything in Blunkett, Bliar and New Liebour's wettest wet dreams.
6) A future government will surely extend and misuse that database: "your car doesn't have an MOT:: no heart transplant for you", "let's sell off the data to that nice Mr Musk/Thiel/Bezos/Beardie/Zuckerberg", "would you like to try our new ad platform google?", etc?
7) The consequences for the individual of a false positive/negative would be devastating.
8) Crapita would get the contract to run it all.
There are bound to be more. These are just the ones that popped up after thinking about it for a second or two.