Olive Woodall, deputy chairman of the environment committee, said: 'It is still an option but I don't think it is likely to be used now.'
Campaigners protested the cull would have killed other wildlife that lived in the warrens. One council member received a death threat.
An RSPCA spokesman said it had been concerned about the use of gas to kill the rabbits. 'It could have been non-selective. We were not convinced by the council's arguments,' he said.
In a statement last night the council's tourism, leisure & amenities director, Ron Cussons, said: 'There has been no change to the previously stated policy on pest control on the Downland. Strutt & Parker, the well known estate and farm management company, have been appointed by Eastbourne BC to implement pest controls on the Downland as required by law. They are using methods which have been in place for ten years including ferreting and shooting.
'Eastbourne BC is working closely with the ministry of agriculture and is carrying out surveys and counts to determine the numbers of rabbits on the Downland.
'No new action is being taken.'