It’s not only at Dover that Brexit is causing delays – on my first trip to Europe since Covid (new Blue British passport in hand), on arrival non-EU nationals had to join a long queue rather than using the automated passport reading route. Plus each non-EU national given the third-degree by border staff, asking what the purpose of their visit was, how long, return flight arrangements, stamping their passport etc. The same thing happened on departure, with separate queues for EU and non-EU nationals.
All this was entirely predictable as a result of Brexit; the EU States have an obligation to ensure that no undesirables enter their territory – once an individual enters an EU country they effectively have access to all EU countries without further checks.
Perhaps for UK nationals, EU countries could have one queue for those who voted for Brexit and one for those who did not.