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The company's six airports handled a total of 9.9 million passengers up 4.4% on the June 2010 total.
Heathrow handled 6.1 million passengers last month, a 6.3% rise on June 2010 and the west London airport's busiest-ever June.
There was a big rise in the number of people flying to Brazil from Heathrow, while US destinations also did well.