Easyjet said border delays caused by the implementation of the new European Entry / Exit System (EESS) were “unacceptable”.
The system was brought in in October last year.
This week, the UK government updated its guidance to people travelling to the European Schengen area, telling them they might need to register their biometric details such as fingerprints and photos when they arrived.
It said people “do not need to take any action before they arrive at the border, and there is no cost for EES registration”.
“EES registration is replacing the current system of manually stamping passports when visitors arrive in the EU.
“EES may take each passenger extra time to complete so be prepared to wait longer than usual at the border,” it added.
A spokesman for Easyjet said: “We are aware that some passengers departing from Milan Linate today experienced longer than usual waiting times at passport control and we advised customers due to fly to allow additional time to make their way through the airport.
“We have been doing all possible to minimise the impact of the airport queues, holding flights to allow customers extra time and providing free flight transfers for any customers who may have missed their flight including EJU5420 to Manchester.
“We continue to urge border authorities to ensure they make full and effective use of the permitted flexibilities for as long as needed while European Entry / Exit System is implemented, to avoid these unacceptable border delays for our customers.
“While this is outside of our control, we are sorry for any inconvenience caused.”