Airlines planning to operate the A380 at Heathrow include Singapore Airlines, Emirates, Virgin Atlantic, Qantas, Qatar Airways and Malaysia Airlines.
America is right to demand more open access to Heathrow, the world's biggest and most lucrative international hub, which is now restricted across the Atlantic to a small club of airlines known as the Heathrow Four: United Airlines, American Airlines, British Airways and Virgin Atlantic.
At present, only four airlines can offer flights between Heathrow and the US and more airlines from the two countries want access to the lucrative market.
Labour peer Lord Soley, who has campaigned for the expansion of Heathrow, said that Chinese airlines had "asked repeatedly for more landing slots at Heathrow" and had been told that their requests would be considered in a review.
He said the CAA issued its ruling on the charges Heathrow could impose on airlines for that period, on the basis of the west London airport handling 78m passengers a year by 2013, more than 8m out.
At present, only two British and two American carriers are allowed to fly transatlantic from Heathrow, the airport most airlines and passengers want to use.
But now that Open Skies has allowed Heathrow airport to open to other airlines, the way should eventually be clear for a deal.
The biggest challenge to the incumbent airlines operating out of Heathrow will come from carriers in the SkyTeam alliance, that includes Air France and KLM, Delta Air Lines, Northwest Airlines News, and Continental Airlines.
British Airlines and Virgin Atlantic, the only two EU airlines currently operating transatlantic flights from Heathrow, have criticized the deal.
But because prices are capped at Heathrow, there has been little motivation for airlines there to move flights to less popular airports.
The Americans are delighted because it means that far more American airlines can expect access to London Heathrow, the world's busiest international airport.
ECONOMIST: Why the Americans are happy and the British are moaning
British Airways cancelled several short-haul and domestic flights from Heathrow Airport on Sunday night, and both Heathrow and Gatwick advised travellers to check with airlines before leaving home.
The treaty puts an end to the exclusive arrangement granted to British Airways, Virgin Atlantic, United Airlines and American Airlines to fly transatlantic out of London Heathrow.
Heathrow wants regulators to allow it to increase charges for airlines to use the airport, between 2014 and 2019.
American Airlines said its flight from Chicago landed at Heathrow at around 8:30 a.m. and that another Chicago flight had arrived at Birmingham.
In making its ruling, the commission decided that the lack of competition in the south-east of England, where BAA also operates Heathrow, and in lowland Scotland was bad for passengers and airlines.
When previous applications were blocked, the so-called Bermuda 2 Agreement was in place, whereby only four airlines, British Airways, Virgin Atlantic, United Airlines and American Airlines, could fly the transatlantic route out of Heathrow, an agreement that the United States government was keen to scrap by putting the hefty conditions on BA's application.
U.S. airlines will vie with BA, the dominant carrier at Heathrow, that currently has flights to 24 U.S. cities.
The big airlines had warned failure to consider a new runway at Heathrow would make the aviation industry go the same way as shipbuilding and coal mining.
BBC: NEWS | UK | Northern Ireland | Late night Belfast flights plan
The two governments could have insisted on one immediately, at the same time dropping their outdated limits on foreign ownership of airlines and releasing take-off and landing slots at congested Heathrow.
It shows just how bad things are if even Lufthansa, one of the world's most powerful airlines, cannot see how to make money by bulking up at Heathrow, one of the most coveted bits of real estate in aviation.
Airlines are giving priority to high-yield business routes to and from Heathrow.
Liberal Democrat peer Baroness Kramer, who campaigned against a third runway at Heathrow when she was a west London MP, called for pressure to be put on airlines to move night flights to after 6am whenever possible.
The travel chaos rippled across Europe as many airlines, including Air France, Alitalia, Lufthansa, Iberia and Aer Lingus canceled flights to Heathrow.
"Heathrow faces stiff competition from other European hubs and we must continue to improve the service we offer passengers and airlines, " Mr Matthews added.
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