Bosses at Heathrow have said they cannot confirm when passengers still waiting for bags, stranded after a computer glitch, will receive them.
The issues began at Terminal 5 last week and affected thousands of departing British Airways passengers.
Some had to fly without their luggage after the problems meant bags had to be manually processed, which takes a lot longer.
Speaking to Sky News on his first day as chief executive of Heathrow, John Holland-Kaye apologised to customers and said the issues had now been resolved.
However, he could not confirm when customers would receive their belongings, saying: "I can’t give an exact time scale for that, we should have put all of the bags into the system here at Heathrow today that are remaining.
"It will then take a few days for British Airways to manage the process of getting them back into the hands of passengers.
"The best advice would be to contact British Airways to see how we can best do that.
"I would like apologise once again to any passengers who have been affected by this.
"We need to do better and as chief executive, starting today, it’s my determination we should do".
Coleen Rooney was among those affected by the IT issues, which lasted from June 26 to 29.
The wife of England and Manchester United (NYSE: MANU - news) footballer Wayne took to Twitter (Xetra: TWR.DE - news) to vent her frustration, writing: "Feel sick ... just received my 4 cases 2 days late from BA Heathrow to Las Vegas. Opened them all and they have been completely ransacked."
British Airways said it had been in touch with Mrs Rooney to apologise and confirmed it had launched an investigation.
In a statement regarding the delays, a spokesperson from the airline said: "We have been working round the clock to reunite customers with their bags since the airport's baggage system in Terminal 5 first started experiencing IT faults last Thursday morning."