About 16 flights arrive at Heathrow between 0430 and 0600 BST daily
The government has been accused of ignoring the disturbing effects of aircraft noise when the latest night flight regime for Heathrow was adopted.
Three councils are at the High Court to get the Department for Transport (DfT) to reconsider which type of plane, and how many, can land before 0600 BST.
London's Richmond and Wandsworth councils and Berkshire's Windsor and Maidenhead are taking the legal action.
The DfT said its policy followed "extensive" public consultation.
Lawyers for the three local authorities accused the DfT of unlawfully failing to act after it was discovered three years ago that some early arrival planes had been placed in the wrong noise category.
Irrational and disproportionate
Transport Secretary Ruth Kelly's predecessor, Douglas Alexander, "failed to address the statutory test of the effect of aircraft noise or, if he did address it, did so in an irrational and disproportionate manner and contrary to his own policies", said David Smith, counsel for the local authorities.
The law required a fair balance to be struck between the interests of society in general and those of individuals, he told Mr Justice Sullivan at the start of a three-day hearing.
The judge heard that the Boeing 747-400 RR, which is the main type of aircraft used by airlines during the night quota period at Heathrow, had been wrongly classified at too low a noise level.
The councils argued, by not acting on the discrepancy, the government failed in its duty to protect residents from excessive noise at night.
There are about 16 early morning arrivals each day between 0430 and 0600 BST.
The court challenge is supported by Kensington and Chelsea, Hammersmith and Fulham, Hounslow and Hillingdon councils and the Greater London Authority.
All the councils are members of the 2M Group which opposes Heathrow expansion.
Meanwhile, mothers and children have planned to protest in central London's Parliament Square against Heathrow's proposed third runway.
One protester, Four Weddings And A Funeral actress Anna Chancellor said: "How can we be expanding our airports at a time when the planet's future is at stake?
"It's criminally irresponsible and the government has got to wake up and start listening."
Members of environmental group We Can will form the shape of a giant "no" and hand a letter to Prime Minister Gordon Brown.
A DfT spokesman said: "The case is being heard this week and it would be inappropriate to comment further."
The hearing continues.