March was the second month in succession that Heathrow handled a record number of passengers this year, despite a fall in transit travellers.
The early Easter boosted numbers as almost seven million travellers used the London hub last month, an eight per cent year-on-year increase.
A total of 936,000 passengers over the bank holiday made it the airport’s busiest Easter weekend ever.
Good Friday was a record direct departure day with 118,000 people flying out.
But the number of transit passengers has been reduced due to £10 government Electronic Travel Authorisations (ETAs) applying to those in airside transit.
Heathrow warned that the policy “will put UK airports at a competitive disadvantage compared to EU hubs”.
The airport said: “While we support the overall rationale behind the introduction of ETAs, we are already seeing an impact.
“In the first four months of ETAs being in place 19,000 fewer transit passengers travelled from Qatar, with the transfer route recording its lowest monthly proportions for over 10 years each month since the implementation of ETAs.
“This is a huge blow to UK competitiveness as many long-haul routes, which are highly important to the UK’s economy, exports and wider connectivity, rely on transit passengers.
“With more connecting passengers expected to choose other hubs as the scheme expands, minsters need to take action to remove this measure.”
Heathrow chief executive Thomas Woldbye said: “We’re on a journey to be an extraordinary airport fit for the future and it’s great to see the progress we’re making this year with smooth journeys for a record number of passengers choosing Heathrow.
“But to keep up the momentum the government needs to exempt airside transit passengers from the ETA scheme to avoid encouraging passengers to spend and do business elsewhere.
“We need to level the playing field, so the UK aviation industry continues to be world-class.”
He spoke as Heathrow assured passengers ahead of the summer peak that “the focus remains on providing a smooth and strong operation”.
A statement added: “Work continues at pace to optimise our current infrastructure making passenger processes faster, more efficient and more resilient including the £1 billion upgrade to 146 security scanners and ongoing investment in our T2 baggage system.”