Dublin airport is well known for it. There is no CTA only arrivals section in this airport and arrivals to this airport go through regular passport control.
This is because according to Irish law, there is the possibility of immigration control on arrival from the CTA. It's from the secondary legislation
Aliens (Amendment) (No. 3) Order, 1997, which grants immigration officers the possibility of conducting immigration checks on travellers arriving from the CTA. In practice, it was brought about because Dublin Airport was expanded, and so all arrivals passed through passport control without separation into domestic/CTA and non-CTA. The situation still remains despite the large rebuilding of Dublin Airport in the past 20 years, because it allows for much more flexibility in the use of the airport if everyone is funnelled through passport control.
It's the same issue with domestic Irish flights: there is no 'bypass' for them, so they need to approach the desks and say where they've come from. You can show a boarding pass and it's more than enough.
The important thing is that under Irish law, British citizens are not aliens, so there's no obligation to produce a passport or ID card. Photo ID is needed, but that's it, I've entered Dublin before using a bus pass!
I am UK Romanian dual national and showed them my Romanian passport as showing then my UK driving licence felt a bit too much of an 'out there' thing to try as its a regular passport control and CTA arrivals including Irelands own citizens have to go through it.
It's not really an issue. If they doubt that you're a British citizen on declaration, they will simply phone up their UK counterparts and ask them to verify if you're a British citizen or not. The usual practice is that anyone who doesn't use a passport or ID card is usually asked where they've flown from, and if they're a British/Irish citizen. If they've flown from within the CTA, can prove it and the document they hold matches their boarding pass, they'll normally just let you go unless there's something very suspicious, such as the traveller not speaking English or Irish.
I've used my Polish driving licence to enter at Dublin before out of idle curiosity. When they asked, I told them I'm a British citizen that lives in PL and that I flew from the UK. As soon as they heard that I have a soft Scottish accent, they were more than happy to let me through with no further checks. Obviously it helps having a British name and Aberdeen as the place of birth on my driving licence, but generally speaking, they're not really bothering people who are obviously Brits.
BBC reporting that EES in Dover Port will be pushed back to next year for most.
I'm led to believe that they're adopting a very cautious approach to the EES in some countries, because they're simply not sure if their systems can handle a huge amount of daily registrations. I suspect that they will keep the existing arrangement for coaches and trucks until the last minute, possibly with some cars being selected to use the new controls until they're fully in place.
The major issue is going to come when the EES is fully operational and the Port of Dover needs to deal with the inevitable large group of travellers who haven't been through the Western Docks for the EES registration. EU travellers won't have to bother with this step, but I suspect there will be considerable jams caused by non-EU citizens who haven't registered in advance and who won't be able to pass through the French border control as a result.