Isn't that what a passport is for?
Seems to me the issue is on the EU side not the UK side, the UK hasn't changed anything has it?
The UK stopped accepting ID cards . Most EU citizens do not possess one because they don't need one unless they travel outside the EU/Schengen. They are generally free and have all your information on them including fingerprints etc rather than pay around €100 for each member of the family for a passport.
Anyway all that did was reduce tourism and deliveries to the UK but is not directly connected to the further delays at Dover after this system has been introduced.
So the EU have long set about setting up a system, which the UK were part of developping, which monitors all the details of the person entering the EU/Schengen, criminal records, how long their stay has been etc, where they are staying etc. Of course, before Brexit, UK citizens had freedom of movement in the EU which they voted against and instead voted for this.
So to get into the system they have put all their details online first to get the visa which costs €7 I believe and then be photographed and fingerprinted at the point of entry in the EU.
There are many illegal British immigrants in the EU, who on the whole have overstayed the 90 days/180 days , some by years.
In most places the system will be manageable , at airports etc, but at bottlenecks like Dover it will be difficult, to say the least. The queues will be on the UK side, not so on the EU side, and thus is a major problem for the UK - which they voted for. So many things the electorate voted for without realising it.
31st January sees inspection of goods coming from the EU which has already been delayed numerous times. More cost and paperwork for the UK.
2024 will see more things to come and will be the start of the turning point where they finally realise the huge mistake they made. So far it's been "Well the sky hasn't fallen in - yet"