In a letter, Charlie Cornish said he "cannot apologise enough" for the delays and the group will "get back to where we need to be soon".
"First and foremost, I want to say that I understand passengers’ frustrations with the queues and congestion they’ve experienced in recent weeks, and I apologise to anyone who has been affected by the disruption," Cornish added.
"We are committed to getting customers away on their trips, especially as we know many have waited such a long time to get back to travelling internationally.