The world’s busiest hub explains the figure was mainly driven by intercontinental traffic, and beat the 34.4 million handled last year.
Net retail income per traveller was £6.42, up 2.2% on the £6.28 that was recorded in 2013.
Heathrow says there was also ‘steady’ start to the new regulatory period with revenue up 7.4% to £1.23 billion, and EBITDA was up 15.4% to £704 million.
Cash generated from operations was £659 million, while pre-tax profit for the first half of 2014 was £47 million.
Highlights in the first six months, included the opening of Terminal 2 by the Queen, and its submission to the Airports Commission to build a third runway.
Heathrow CEO, John Holland-Kaye, explains: “Heathrow has performed well over the last six months, with two consecutive quarters of record passenger satisfaction scores reflecting steady operational improvement.
“Terminal 2 successfully opened on time and on budget, marking the next step in the transformation of passenger service at the airport.
“My vision is to build on that record of continuous improvement, driving Heathrow to win the case for expansion and become one of the best airports in the world – an ambition which will give the UK a great springboard to continue to compete successfully in the global economy.”