Heathrow praised the way its check-in process worked in May despite huge queues over the Jubilee and school holiday weeks.
It was its busiest month since the pandemic started, added the airport, with 5.3mln passengers or around 79% of the number in May 2019.
That was nearly an eight-fold increase when compared to May last year, when the UK's Covid-19 travel restrictions were in effect.
Airlines and airports faced widespread anger after holidaymakers suffered delays and cancelled flights.
As government and airlines played the blame game several flights were cancelled during the extended platinum jubilee holidays and passengers were left stranded.
But the airport said no more flights were cancelled at short notice than on a typical day and Border Force performed well during the month.
It said resources remained tight, but work was being done to "match supply and demand", which made a big difference over Easter and the half-term holidays.
The airport said criticism of other airports had vindicated its plan to "maintain high levels of passenger service".
"I’m immensely proud of the way my team has worked with airlines and other partners to ensure passengers got away during the jubilee half-term," said Heathrow chief executive John Holland-Kaye, reports Guardian.
"We continue to make good progress with our plans to ramp up capacity and are working closely with airlines and government to keep supply and demand in balance as we grow, so that passengers can travel through Heathrow this summer with confidence."
With more passengers checking in online, 90% of passengers went through security in under 10 minutes at the UK's biggest airport in May.
In the next step to up capacity, Terminal 4, which was closed due to the virus crisis, reopens on Tuesday before the summer peak and will initially be used by 30 airlines.