The fact that the UK doesn’t allow “impromptu checks”, otherwise known as “Papers please!” is not a bug, it’s a feature that distinguishes our democracy from other states and we are pretty proud of it.
There is nothing undemocratic about checking whether you are compliant with employment regulations on a regular manner anymore than it is to check whether your gas installation is compliant with gas regulations or your voting registration is compliant with voting policy. It is completely orthogonal. You might not be in favour of a policy but that does not mean that the policy is undemocratic.
In times of war, civil liberties get curtailed. And in 2025 when Russian and Chinese bots are interfering in our democracy at an industrial scale to destroy our countries from within, the idea of identity being overlooked for all aspects of public life is looking increasingly untenable.
In the UK you do not have to have your drivers license upon your person when driving a car. Usually you'll be instructed to present it to a nearby police station within a few days.
Not required by law in the UK to have ID on you while driving. Works well enough (you have to produce it at a station within 7 days). I'm sure if it's serious enough, the police can force some other method