> some sort of number provided by the government

There are countries where each citizen has one unique identifier (Sweden's "personnummer", Denmark's CPR).

The UK is definitely not one of those! [yet]

Instead there are many different identifiers, each for a different purpose, and stored in different systems which almost certainly don't talk to each other.

Just for starters: NHS number for healthcare, National Insurance number for social security and pensions, Unique Taxpayer Reference for tax, Passport (with a number that changes when you renew your passport), Driving licence (with a "number"[alphanumeric] which stays constant even when you renew)...

Multiple overlapping identifiers... and I may have missed some :)