They're seeking a ban on approaching the airport by 5 million people and this will include the Piccadilly Line, Heathrow Express & parts of the M25. See The Guardian, for more on this. Personally I don't see how this will be possible, as although they're aiming at the protesters including the National Trust, Woodland Trust, RSPB supporters, members of Greenpeace, Friends of the Earth and the Campaign to Protect Rural England - the injunction if carried out would effect anybody trying to get to the airport.
According to Greenpeace "'a source' who's spoken to BAA has just told us that BAA is deliberately making the ban as broad as possible, and leaving it up to the police to apply it with common sense. Which means, if BAA wins, the police will have the right to stop you, me or Her Maj from, say, getting on "all railway trains and carriages operating upon the Piccadilly line".
Sheriff Ken is none too happy about this and said "I regard BAA's proposed injunction as a serious infringement of civil liberties and an attack on the right to peaceful protest. It could have a significant impact upon London Underground operations. BAA did not consult Transport for London about this proposed injunction. Transport for London will be writing to BAA to demand that all reference to its property and services be removed from any such injunction and will oppose any attempt to restrict the lawful use of its public transport services in the courts."
In the meantime there's a party on the Piccadilly Line this Tuesday 31st July if you feel like a protest. If you have a Facebook account you can find out more about that here.
BTW - the commenting function with haloscan seems to be a bit screwed up at the moment although it works in IE but not in firefox (weird)