It's a two-way exploit. The workers are exploiting a weakness in the system.

In the US, we have somewhat of a similar problem. Individual states can license noncitizens for driving. This acts as a form of identification, which somewhat legitimizes their status. The federal government has required states to issue "Real ID", which also checks for citizenship. Those who are get a gold star on their license. Real ID is also needed to board domestic flights.

The closest we have to a national ID is a passport, which you can get as the traditional book passport and/or a passport card. The passport card is useful for crossing back to the US from Canada and Mexico, and for boarding domestic flights. But it's also accepted as ID for other purposes. I generally use the card as it does not have my home address like the driving license does. And the passport card is only issued to citizens. I got both passports with one application.

The passport card is mostly useful for the border crossings mentioned and for sea crossings to the Caribbean and Bermuda. For other travel, the traditional passport book is necessary.

Perhaps the UK would save setting up an entire infrastructure on setting up for a national ID by offering a passport card. This way citizens would only have to apply for one or both types at the same time. They've already done the work of verifying citizenship.