Heathrow capped daily passenger numbers at 100,000 last month and told carriers to stop selling seats for the period through to 11 September.
It is, though, thought flights will remain capped for the rest of the summer season.
The airport on Thursday (11 August) said the cap had delivered improvements to passenger experience with fewer last-minute cancellations, as well as better aircraft punctuality and baggage delivery.
It also claimed to have experienced the largest rise in passenger numbers of any European airport in the past year.
More than six million people travelled through Heathrow in July, with a total of 16 million expected in the three-month period to the end of September.
“Passengers are seeing better, more reliable journeys since the introduction of the demand cap," said Holland-Kaye.
"I want to thank all my colleagues across the airport for their amazing work in getting people away on their holidays. This has only been possible because of the collective and determined efforts of airport, airline and wider Team Heathrow teams."
Heathrow said lifting the cap was dependent on increasing airline ground handler capacity "and resilience". "We have initiated a review of ground handling to support that objective," said Heathrow.
However, while the airport has repeatedly laid the blame with ground handlers, the boss of Menzies Aviation in July said the key role they play has been under-appreciated by government and the airport sector.
Elsewhere, Heathrow said after recruiting an additional 1,300 people, security resource at the airport was back to pre-pandemic levels – a process that got under way last November. According to the airport, 88% of Heathrow passengers are clearing security in 20 minutes or less.
Additionally, it said Border Force "had performed well so far this summer". "We are working to help them secure sufficient resource to serve the peak in passengers returning to the UK over the next few weeks," the airport added.
