The court challenge is part of a joint effort by a number of councils, The Mayor of London and Greenpeace, to stop the third runway.
They have formally notified the Secretary of State for Transport that they will seek a judicial review on the grounds of air quality, climate change, strategic environmental assessment, including failing properly to deal with the noise consequences, and surface access impacts.
The challenge comes soon after the councils warned that
a third runway may result in noise from 63 flight arrivals or departures at Heathrow before 5am.
On surface access, the councils' concerns include that the plans fail to recognise the scale of the challenge to accommodate additional traffic movements without unacceptable effects on the transport network and unacceptable effects from traffic pollution.
Speaking on behalf of the group, Cllr Ray Puddifoot, Leader of Hillingdon Council, said: "We have given the Government numerous opportunities to address our concerns and answer our questions and they have demonstrably failed to do so.
"The Government has misunderstood and misapplied the law on air quality, despite having already lost recent legal challenges on this issue.
"The evidence of unacceptable damage to the environment and the health and wellbeing of many thousands of people is untenable in both law and common sense."
The Government must now respond to the councils' formal letter before action. If the Transport Secretary does not agree to a quashing of the plan, then the local authorities will bring judicial review proceedings.
The local authority group comprises the London boroughs of Hillingdon, Wandsworth, Richmond, Hammersmith & Fulham, Windsor and Maidenhead Council, The Mayor of London and Greenpeace.
Hillingdon has support from leaders of Wandsworth, Richmond, and Windsor & Maidenhead councils for a possible judicial review, if proposals go ahead.
Cllr Ray Puddifoot. Leader of Hillingdon Council, said: “The ill-health consequences of a third runway are frightening. If it’s not worsening air quality from increased road traffic, it’s disruption to sleep patterns from early morning noise.
“The Government has failed to assess the true health impacts from expansion and it has failed even to identify which communities will be affected.”
He said: "Throughout the whole consultation process, the Government has failed to address the concerns not only of the impacted communities but also the advice from the Transport Select Committee. Now is the time for councils and groups to come together to stop this in the only way left to us - the courts. We are delighted the Mayor is joining and urge other boroughs to do the same.”
The DfT and Government have said Heathrow expansion is crucial for the economy and tourism.
Officials said there would be a “world-class package of compensation and mitigation measures to support those affected by the expansion, with up to £2.6 billion for compensation, noise insulation and community amenities, which could include improvements to parks and leisure facilities” if it goes ahead.
A statement read: “These are reinforced by plans for a 6.5 hour scheduled night flight ban and noise restrictions which will be legally enforceable.
“To make sure the whole of the UK benefits, the government has committed to about 15% of slots for domestic routes. While many of these will be delivered commercially, government has for the first time set out that it would use public service obligations to ensure existing and new routes are safeguarded.
“This includes the potential for slots to be ring-fenced and exempt from air passenger duty, which can save passengers £26 on the cost of a return domestic ticket.”
The DfT added: “The government is confident that the scheme can be delivered within our obligations under the Climate Change Act, and development consent would only be granted on the basis that the new runway is delivered within existing air quality obligations.”