Source: Sharecast
A record 7.2m people used the west London airport - Europe’s busiest - last month, a 0.4% uptick and the strongest ever May.
Heathrow said it had benefited from a "strong" late bank holiday as well as Manchester United and Tottenham Hotspur playing in the Europa League final in Bilbao.
It said 22 May, the day after the final, had been a record. A total of 16 flights operated across the two days, double the norm.
In the year to May, 84m people used the hub, a 3.1% increase.
However, Heathrow also called for an "honest conversation" about increasing capacity.
It said: "As these record numbers become the norm, it’s time to start an honest conversation about the challenges this presents for an already space-constrained yet highly efficient hub.
"Heathrow continues to deliver excellent service, but to sustain this performance and meet future demand, expanding capacity will be essential."
Earlier this year, chancellor Rachel Reeves said the government would support an expansion of Heathrow, despite long-standing opposition from local and environmental groups. Heathrow has since announced plans for a "phased" expansion, which will start with upgrades to existing sites, including reconfiguring the layout of the airfield and expanding terminals 2 and 5.
It is then expected to apply for permission to build a controversial third runway later this summer.
While Reeves has made it clear the government is minded to approve a third runway, however, London mayor Sadiq Khan and transport committee chair Ruth Cadbury have already been vocal in their criticism.
Thomas Woldbye, chief executive, said on Wednesday: "Over the past year, we’ve supported 84m journeys and this summer we’re ready to welcome even more. The fact remains Heathrow is at capacity."
Susannah Streeter, head of money and markets at Hargreaves Lansdown, said: "Neither trade turmoil nor geopolitical conflict put off international travellers, with [Heathrow] posting yet another record month.
"The airport is set to use this continued growth to bolster its argument for a third runway. With Reeves keen to pull all growth levers possible to boost the economy, tapping high interest in globetrotting looks likely to be more of a priority than environmental concerns."