A coalition of councils near the airport, plus Greenpeace UK and a local resident claimed the decision to permit the new runway was unlawful because residents were not consulted despite a promise made by former Prime Minister David Cameron that development would not go ahead.
The objection is also based on claims that the government has not taken into account the unlawful air quality that development will allegedly bring.
Lawyers for Transport Secretary Chris Grayling argued successfully that a judicial review could not proceed until after a National Policy Statement on aviation is published later this year or in 2018.
It is though to be the first legal challenge to plans to expand Heathrow following the decision to give the go-ahead to a third runway. Opponents are likely to resume the court battle once the National Policy Statement is published.