The owner of Heathrow Airport, BAA, is seeking an injunction to ban protests by environmental groups opposed to plans for a third runway.
BAA owns seven airports in the UK
The Independent newspaper reports that the injunction would mean members of 15 groups could be arrested at the airport or on road or rail routes to it.
Civil liberties groups say it would put new limits on peaceful protest.
BAA insists it is seeking the ruling "to protect the operation of the airport and the safety of passengers".
Direct action by "green" groups under the banner Camp for Climate Change was planned between the 14 and 21 August.
Organisers hoped as many as 5,000 people would take part, spending a week in tents outside the airport.
A spokesman for BAA said 200,000 people a day passed through the airport during the busy August period, adding: "It is these people who would suffer as a result of any unlawful or irresponsible behaviour.
"We respect people's right to protest within the bounds of the law and airport bylaws, and we would invite protesters to similarly respect the rights of passengers travelling through Heathrow."
The Independent says the injunction requests the right for police to arrest anyone who fails to give 24 hours' notice of a protest.
They could be detained, the paper says, on sections of the M4 and M25 motorways, including service stations, which lead to Heathrow, and platforms six and seven at Paddington Station which serve the Heathrow Express rail service.
Mayor of London Ken Livingstone has also reacted angrily to the news that the Piccadilly underground line which runs to Heathrow would also be covered by the injunction.
"I regard BAA's proposed injunction as a serious infringement of civil liberties and an attack on the right to peaceful protest," Mr Livingstone said.
"It could have a significant impact upon London Underground operations."
He said he would be demanding BAA remove all reference to Transport for London property and services from the injunction or face a challenge in the courts.
GROUPS FACING THE BAN
Camp for Climate Action
No Third Runway Action Group
Aviation Environment Federation
Friends of the Earth
The Woodland Trust
World Development Movement
National Society for Clean Air and Environmental Protection
The injunction is reported to have been served on Monday on the leaders of four campaign groups.
Among them is Airport Watch, an umbrella group which includes The Woodland Trust, the Campaign to Protect Rural England (CPRE) and Friends of the Earth.
Civil rights group Liberty said the injunction was an example of a "dangerous and undemocratic trend" by large companies to seek to limit the right to protest.
Leo Murray, from pressure group Plane Stupid, told BBC Radio Five Live he thought BAA was afraid of negative criticism.
"BAA are pretending that this is about protecting passengers or preventing some sort of security scare, " he said.
"But the reality is what they're really afraid of - and they should be worried - is thousands of people who are armed with peer-reviewed science which shows that their plans for expansion are totally incompatible with our plans for preventing climate change."
BAA said it had proposed several alternative sites at the airport "for the purposes of lawful and peaceful protest" which would be discussed at the injunction hearing.
The company, which owns seven UK airports, will go to the High Court next Wednesday.