Hundreds of Travellers living in the greenbelt in Essex can be forcibly evicted from their site on Thursday, after their failure to win a last-minute injunction in the high court.

A judge ruled that the planning system had been "efficient and fair" in taking eight years over the case and allowing numerous appeals. Basildon borough council could now evict the 400-strong community who had set up caravans at Dale Farm over the last 10 years.

But Mr Justice Kenneth Parker said he had concerns about the health of one Dale Farm resident, 72-year-old Mary Flynn, and asked the council to provide assurances in the next seven days that her poor health would be taken into consideration before eviction.

The Travellers on Wednesday confirmed they would appeal against the rejection of their injunction to halt the eviction.

Campaigners said the judge's order saying Basildon council had time to assess Flynn's health first, gave the Travellers the chance to do a health audit on the site.

Candy Sheridan, a campaigner for the Travellers, said: "Mary Flynn is one of many with real serious health problems. We've got people dying of cancer and we've got people on dialysis."

The Travellers claim that the health of Flynn has "substantially deteriorated" since the last appeal against their eviction and that she has a right to private and family life at home under Article 8 of the European convention on human rights.

But Parker said the Travellers had come "to the end of the road" of their appeals.

"It is in the public interest that there should be finality to litigation," he said. "I find no exceptional circumstances in this case that would justify the reopening of a judgment given by the court of appeal relatively recently, having specifically considered the challenge made under Article 8 of the convention."

Vanessa Redgrave, who was in the courtroom, said considerations about the greenbelt and traffic had been put above human rights. "The greenbelt and the environment have won over the communities and lives of human beings who have not actually disturbed the greenbelt. This should never have come to court. Dale Farm should have been left where they were and encouraged and not be ruled against ever time they tried to get it sorted out."

Kathleen McCarthy, a Dale Farm resident, said the authorities needed to realise what they were doing when they claimed to be "cleaning up" the site with the eviction. "When you're cleaning up something you're cleaning up rubbish, so they're trying to say that we're rubbish," she said. "We are definitely being victimised."

Despite the council having the right to clear the site from midnight, Tony Ball, leader of Basildon council, said they would do that only after giving the Travellers a starting date. "Direct action to clear Dale Farm is a last resort … and we take it reluctantly – but after almost 10 years of legal wrangling and exhausting the judicial process the Travellers have left us with absolutely no choice, they have broken the law, which we are duty bound to uphold. And this is what we believe the vast majority of local people expect us to do."

The council says it will house vulnerable members of Dale Farm but residents say they want to live in caravans with their extended families, not get "bricks and mortar". Most of the 86 families say they have nowhere else to go and will be forced to stay illegally by the roadside.

Ten pitches for Travellers have been offered by a landowner near Stowmarket, Suffolk, but most local councils in East Anglia are understood to be keen not to allow an influx of Travellers from Dale Farm into their area.