Heathrow says the charges, which need to be approved by the Civil Aviation Authority (CAA), will help pay for £3 billion of investment, including the opening of the new Terminal 2 next year.
Airport bosses said that errors in previous passenger forecasts meant that Heathrow had lost out on around £650 million of charges over the last five years.
The CAA had based the previous level of charges on estimates that Heathrow would handle 78 million passengers a year by 2013, but the airport is only handling around 70 million.
More top news
Brent Council is offering to cut business rates for firms that pay the London Living Wage.
A man standing trial accused of murdering two pensioners has been found hanging in his prison cell, police say.
Bees Number One is 'best in the league."