Fifteen men suspected of being kept as "slaves" at a travellers' site in Bedfordshire are still being treated for malnutrition and medical problems.
Nine British and eastern European men also found at Green Acres caravan park near Leighton Buzzard on Sunday have refused to help the police inquiry.
Four men were arrested when the victims, suspected of being kept against their will, were found.
A pregnant woman, who was also arrested, has been released on bail.
The woman will be questioned further following the birth of her child which is imminent. Inquiries to locate two further suspects are under way.
Some of the 24 people found in squalid caravans and sheds were covered in excrement, police said.
Police believe they had been approached at benefits offices, job centres and soup kitchens and were allegedly offered work at £80 per day, but when they arrived at the site they received no money.
It is suspected some had been there for as long as 15 years.
Their heads were shaved and they were given little or no food, and they were allegedly threatened if they tried to leave.
A police spokeswoman said: "Nine of the men have left a medical reception centre and have chosen not to support the police investigation.
"At the moment, the remaining 15 continue to be assessed for medical and welfare needs.
"It will take a number of days to establish exactly what has happened to them while living on the site."
The victims assisting the investigation include eight British men, three Poles, a Latvian and Lithuanian plus two further men whose nationalities are as yet unconfirmed.
They are all aged between 30 and 57, with the youngest and oldest both British.
Those who chose to leave police care were seven Britons and two Romanians.
The youngest person found on site was a 17-year-old British man who has now re-joined his family.
The men arrested have been detained on suspicion of slavery and servitude offences under section 71 of the Coroners and Injustice Act.
Police have appealed for help and asked anyone with any information to contact them in confidence.
More than 200 officers raided the travellers' site at Great Billington at 05:30 BST on Sunday.
The move was part of a long-running investigation by Bedfordshire Police which suggested the men were being held against their will in poor conditions at the site, and forced to work for no pay.
Det Ch Insp Sean O'Neil said: "Those people who we continue to help are appreciative of the support that is on offer but it will take some time to work through with them what has happened.
"I am confident that while the investigation is in its early stages this is a family run 'business' and is an organised crime group that has been broken up by the Netwing operation."
Operation Netwing is being led by Bedfordshire Police, supported by the local and health authorities and other agencies as well as the Human Trafficking Centre at the Serious Organised Crime Agency.
The British Red Cross said it is providing support to the people who were allegedly held against their will at the site.
Melissa Magna, the Essex branch's community services manager, said: "British Red Cross volunteers are trained to provide practical and emotional support to people in a crisis.
"We are checking on the individuals' welfare and giving them the practical help they need, such as providing clothing, hygiene kits including towels, blankets, emotional support, and recreational activities such as games, radio, DVDs.
"We are also providing first aid cover and assisting with registration and serving food and drink. We are providing a 24/7 presence for the duration of the rest centre."
Speaking in the House of Commons earlier, South West Bedfordshire MP Andrew Selous called on the government to look at the issue of internal trafficking within the UK.