Queues of up to four hours have been reported since the introduction of more stringent checks on travellers entering and leaving the Schengen area, which allows passport-free movement across much of the EU.
Airports in Portugal, especially in Lisbon, Spain, France, Italy and Belgium have been affected.
Airlines For Europe (A4E) had warned last weekend would be one of the busiest of the year with 10 million people passing through European airports on Saturday and Sunday combined.
British Airways, easyJet and Ryanair all alerted passengers to the need to turn up at airports earlier than normal.
Ryanair issued an alert which urged its customers to arrive “at least three hours before the scheduled departure time”.
BA sent text messages to passengers flying back from airports where long lines at border controls were expected.
A spokeswoman said: “We’re texting customers flying from airports that we know are having issues to ask them to arrive early.”
The carrier has promised that any customers who missed their flight because of the queues would be re-booked for free.
The extra security measures were brought in following terror attacks in Paris and Brussels.
They have led to long lines at border controls as the details of passengers from non-Schengen countries - such as the UK - are run through databases to alert authorities if they are known to pose a threat.
Ryanair boss Michael O’Leary said recently that more than a fifth of the airline’s flights were being delayed because of the issue and he is “jumping up and down” in frustration.
Just 78% of the Dublin-based carrier’s flights were on time on Tuesday, down from 90% during the month of August as a whole last year.
British Aviation minister Lord Callanan has been in touch with other governments over the issue.
“I hope it’s teething problems,” he said. “We are certainly in contact with other governments across Europe to do all we can to mitigate them and to make it easier for people who are trying to enjoy their hard-earned break abroad.”
European Commission spokeswoman Mina Andreeva said there was a “price to be paid” for security, but insisted that EU countries should have put arrangements in place to avoid lengthy queues.
At a press briefing in Brussels, she said: “We understand there are concerns about EU rules that might lead to longer waiting periods. But this is very clearly about the security of our citizens and it is member states that have called for these rules, unanimously, in the European Council in October 2015.”
She added: “There is always a price to be paid for security and also member states had enough time to prepare for the entry into force of these rules.”