The dispute flared when the 70 councils in the LGA's Strategic Airport Special Interest Group made a last ditch call to the government to look again at sites for a new airport in the Thames estuary.
Next week, ministers are expected to issue a white paper that will opt to expand existing airports, a move affected councils would strenuously oppose.
The group complained that the government had ditched proposals for a new airport at Cliffe, on Medway's Hoo peninsula, and ignored two plans for nearby sites also in Medway that would have less environmental impact.
'No one in their right mind would consider developing an airport in the Thames estuary.
'It would cost even more than the Cliffe option and would be just as environmentally damaging.'
Mr Chambers dismissed as inadequate an LGA statement that special interest groups represent only their members, not the association.
SASIG director Jim Bailey said the government should delay the white paper while it considered fresh research conducted by the group on the estuarial sites.
'The right solution is a new airport, but at a better site than Cliffe,' he said.
Many SASIG members would be affected by expansion at Heathrow or Stansted. Legal problems prevent expansion at Gatwick until 2019.
Uttlesford DC leader Alan Dean (Lib Dem) said: 'It is not just a matter of damage to the local environment.
'The aviation industry has got to be brought under control and the arguments on global warming are very important.'
A spokeswoman said Hillingdon LBC was 'strongly opposed to any third runway at Heathrow', which would require the demolition of nearby homes.