An elderly resident is being given a final chance to challenge the clearance Dale Farm travellers' site at Crays Hill.
Earlier today Mary Flynn, from Dale Farm, was refused permission to go to the Court of Appeal after a judge read the case papers in private.
Later a spokeswoman for the Judicial Office announced Mrs Flynn was renewing her last-ditch application at an oral hearing in open court on Monday - the day the clearance is due to begin - before Lord Justice Pill.
No formal "stay" was granted today to halt the clearance, and it was unclear whether Basildon Council would delay starting evictions pending the appeal hearing.
Normally local authorities do not act until legal proceedings have been exhausted.
The eviction follows a decade-long row over unauthorised plots.
Although half of the site is legal, an estimated 400 people are said to be living on 51 unauthorised plots Small numbers of Dale Farm travellers have left the site ahead of the clearance, but others have said: "We're staying put."
Residents' hopes of appeal judges overturning a High Court judge's refusal to grant a temporary injunction blocking the evictions are pinned on 72-year-old Mrs Flynn and concerns over her health.
She suffers breathing problems and uses an electric nebuliser and has been the crucial protagonist in the High Court battle.
When he refused the injunction application on August 31, Mr Justice Kenneth Parker said the only aspect which gave him some concern was medical evidence received of significant deterioration in Mrs Flynn's condition.
The judge was told by lawyers for Basildon Council that this fresh material would be considered before proceeding against her.
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