Heathrow recorded a 2.5% growth in passengers in March compared with the same month last year.
Figures released by the west London airport show that 6.1 million travellers used the hub last month.
The growth was driven by emerging markets, with China up 12%, the Middle East 9%, Mexico 6% and India 4%.
Carriers have benefited from new larger aircraft such as the Airbus A380.
Garuda Indonesia launched the UK's first direct service to Jakarta in March.
Heathrow chief executive John Holland-Kaye said: "It's been a record March for Heathrow and I'm delighted that we've added the UK's first direct connection to Indonesia.
"As South East Asia's largest economy, Garuda Indonesia's new route will be a significant boon for British SMEs (small and medium-sized enterprises) looking for new export opportunities."
Some 3.1 million passengers used Gatwick last month, up 5.8% year on year.
Stansted welcomed 1.9 million passengers during March (a 13% rise), while Dubai, Dublin, Amsterdam, Tenerife and Alicante were the most popular international routes from Manchester, which experienced 11% growth to 1.7 million passengers.
Luton Airport recorded 1.1 million passengers last month, a 24% increase year on year.