Opposition to the proposals had been led by groups representing communities around Heathrow, Stansted and Luton BC and Wandsworth and Hillingdon LBCs.
Ministers also failed to make the public aware of serious alternatives to the option of a new airport at Cliffe in North Kent. Having considered two schemes for estuary airports at Thames Reach and Sheppey they failed to evaluate them to the same depth as Cliffe - even though the risk of bird strike meant development at Cliffe was impractical.
A new 24-hour airport in the Thames Estuary would remove the need for night flights over London.
If the court finds that the consultation process was unfair the government could be forced to amend the white paper and run the whole process again.
Wandsworth LBC leader Edward Lister said:
'Our argument is that the government did not reveal the full picture in its white paper.
'People in south and west London never had the chance to comment on the possibility that they might lose the protection of runway alternation.
'We do not think enough attention ahs been paid to the concerns of people who will pay the price for the extra noise generated at these airports.
'It is the duty of local councils to represent their residents' concerns and ensure that proposals for extra capacity are properly weighed against all the alternatives.'
The south and west London councils backing the challenge include Wandsworth, Hillingdon, Lambeth, Kensington and Chelsea and Windsor.
The judicial review is expected to be heard during the next three months. It will also combine separate challenges from a group of local councils in Hertfordshire and Essex.
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Statement from Hillingdon LBC follows:
Hillingdon LBC has welcomed the go-ahead by a high Ccurt judge on Friday for a judicial review of the government's white paper for the expansion of airports in south east England, including a third runway at Heathrow.
Council leader Ray Puddifoot said: 'The council remains unanimously and resolutely opposed to proposals for an additional Heathrow runway.
'A third runway and associated airport development would have a devastating environmental effect on local communities in the borough's airport villages and the wider area.
'We are now able to join with other objectors in challenging the considerable flaws in the White Paper, such as the introduction of the new proposal for a sixth terminal at Heathrow, about which there had been no consultation, and the failure to consult on proposals for take-offs and landings on the same runways rather than separately as at present.'
The other parties to the judicial review are Wandsworth LB, HACAN ClearSkies, Stop Stansted Expansion and the Luton and District Association for the Control of Aircraft Noise.
The hearing is expected to take place in the high court in the autumn.