A coalition of local councils, green groups and residents argued that the expansion decision was at odds with the UK's overall climate change targets.
The coalition includes six local authorities, Greenpeace and the Campaign to Protect Rural England (CPRE).
Today Lord Justice Carnwath, sitting in London, upheld their argument that the Government's policy support for a third runway, made in 2003 and confirmed in January last year, will need to be looked at again, particularly in respect of climate change policy and surface access.
The coalition said in a joint statement that the Government's Heathrow policy "is in tatters this morning".
The statement said: "If the Government wants to pursue its plans for Heathrow expansion, it must now go back to square one and reconsider the entire case for the runway."
Hayes and Harlington Labour MP John McDonnell, who has led the campaign against the expansion of Heathrow for the last 30 years, said: "In essence, this judgment means that the game is up for a third runway at Heathrow and I am calling upon the Government to accept the inevitable and lift this threat to my community."
He went on: "What we need now is a sensible approach to developing a sustainable transport policy based upon high-speed rail.
"This judgment is a victory. It means that whichever party is in government, they will not now be able to force through Heathrow expansion."
But Transport Secretary Lord Adonis reaffirmed the Government's support for expansion, saying he welcomed the court's ruling.
It does not rule out a new runway but calls for a review "of all the relevant policy issues, including the impact of climate change policy".
Lord Adonis said: "Heathrow is Britain's principal hub airport. It is vital not only to the national economy but also enables millions of citizens to keep in touch with their friends and family and to take a well-deserved holiday.
"The airport is currently operating at full capacity.
"A new runway at Heathrow will help secure jobs and underpin economic growth as we come out of recession. It is also entirely compatible with our carbon reduction target, as demonstrated in the recent report by the Committee on Climate Change."
He went on: "The Government confirmed support for expansion at Heathrow only after detailed assessment showing that the strict environmental limits set for expansion could be met. In parallel, we announced measures which will give the UK one of the toughest environmental regimes of any country in the world."
Shadow transport secretary Theresa Villiers said: "Labour's flagship transport policy is in complete disarray. This judgment is a damning indictment of Labour's wholly misguided support for a third runway.
"It is proof that they cannot be trusted to safeguard our environment and that the whole handling of this hugely important issue has been riddled with incompetence and duplicity. They must drop their support for a third runway now."
She went on: "There will be a clear choice at the general election between five more years of Gordon Brown and his exhausted Labour Government or change with the Conservatives who will stop this runway from being built. Today's news shows that the Conservatives made the right judgment and Labour got it wrong."
Liberal Democrat MP Susan Kramer, whose Richmond Park constituency in south London will be affected by any increase in flights and who has led her party's campaign against Heathrow expansion, said: "This is a declaration of victory, the final nail in the coffin for the Government's attempts to steamroll over local and national opposition to its disastrous third runway plans.
"The expansion of Heathrow would be a catastrophe for our climate and for the thousands of Londoners who would be forced to live with the huge disruption it will cause.
"There is no way the Government can tear up what it has already done and start again - because we know the real climate change figures prove that there is no economic case for expansion at all.
"Labour tough talk on climate change is just hot air."
The anti-Heathrow expansion coalition group stressed the importance of today's ruling for the future of air transport generally.
The coalition statement said: "The implications of today's ruling are profound, not just for Heathrow but for air expansion plans across the UK.
"Lord Justice Carnwath ruled that the 2003 Air Transport White Paper - the foundation of expansion plans across the country - is obsolete because it is inconsistent with the Climate Change Act 2008."
The coalition said the judge had also expressed real concern over the "hardship caused to the local community by uncertainty" over the third runway.
In his ruling, the judge said: "Whether there should be a third runway at Heathrow Airport is a question of national importance and acute political controversy.
"It is a matter on which the main parties are currently divided and which may well become a significant debating point at the forthcoming general election.
"The court is concerned only with issues of legality."
The judge said the coalition's submissions "add up, in my view, to a powerful demonstration of the potential significance of developments in climate change policy since the 2003 White Paper".
He said they were "clearly matters which will need to be taken into account" under the new national policy statement (NPS) dealing with airport expansion.
But the judge said he was not able to hold that the points raised amounted to a "show-stopper - in the sense that the only rational response would be to abandon the whole project at this stage".
While ordering reconsideration, the judge refused to quash the Government's decision to "confirm policy support" for a third runway, stating that he doubted whether such an order would be appropriate.
He adjourned the hearing until after Easter to give both sides time to consider what formal orders the court should make.
Speaking after a question-and-answer event with small business owners in Ellesmere Port, Cheshire, Conservative leader David Cameron said: "The (Government's) policy is in tatters. They made the wrong judgment about this, we made the right judgment.
"We said the third runway shouldn't go ahead, we were absolutely clear about that.
"There is no case for it on environmental grounds, there is no strong business case for it.
"What we need is high-speed rail with a rail hub at Heathrow as an alternative - that's the answer, that's what we should be doing, and the Government needs to realise they made a bad mistake, a bad judgment and they need to go into reverse."
The Institute of Directors described the decision as "unfortunate" and said it put at risk "the UK as a major trading country and London as a global business centre".
The IoD has some 50,000 members across the business spectrum, ranging from chief executives of large corporations to those running start-up companies.
Insisting that expansion must go ahead, IoD spokesman Alistair Tebbit said: "This is a very unfortunate decision.
"With the current airport operating at 99% of capacity, Heathrow's status as a global hub for air services is under threat.
"We urge the Government to move as quickly as possible to get expansion back on track.
"It's worth us all remembering that Heathrow is a British success story. In its capacity as the major UK hub for international air services, Heathrow has supported the development of the UK as a major trading country and London as a global business centre.
"Without a third runway we put all of this at risk.
"Of course it's essential that noise and air quality targets are met. But those who raise objections to further development need to recognise that there's no realistic or cost-effective alternative to expansion.
"To provide for the needs of the economy over the next 20 to 30 years we must have a third runway."
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