They would only say how pleased they were to be here, and how much they were looking forward to a bright, new future in Britain.
"Stefan", 33, who would not give his real name for fear of reprisals at home, was discovered in the back of a truck with his wife, three children and 10 other families at Dartford Container Terminal on 26 November. Since then they have been housed in a hotel near Gravesend, a decision that prompted an outcry, before being moved to a council family centre near Sittingbourne.
With them are some of the women and children from the group of 103 asylum seekers who were found at the same terminal last Thursday night.
"We are poor people, gypsies, and we heard that if we came to England there would be a better life for the gypsies," he said, in the chaotic surroundings of the centre where women were preparing dinner as children demanded attention.
Originally from near Bucharest, his group, 35 in total, had been in the Romanian town of Arad when they had found a lorry driver willing to transport them across Europe. By day the men had been working on a big building site, while at night the whole group had been sleeping on the local railway station.
"He saw we were poor people, and felt sorry for the children and said he would take us to England," said Stefan. The Romanian driver had even bought them all food with his own money, he said.
Stefan denied that he had paid anything to the driver or anyone else for the journey. Asked if any of the group had paid, he shrugged and said he did not know.
The trip had taken a week in the back of the cold truck, after which the driver had directed them into another lorry that was going to England by ferry. "I really had no idea where we were going or where we had been. We could have ended up in Yugoslavia for all I know.
"But then the police opened the back of the lorry and we were in England," said Stefan. "It is a miracle."
He said they had been found at 4am after officers had heard the children making a noise. "The police were very nice. They took all the babies from the truck nicely and gently," he said. "It is a big difference between here and Romania."
Harassment of gypsies there had got progressively worse since the fall of the Ceausescu regime, he said. Police would come through their houses, take men away and lock them up for three to four days at a time with no explanation.
Now, however, he thought the future would be better: "I believe I will now get a house, the children will go to school, I will get a job and I will be happy," he said.
And if he were to be sent back? "I had better hang myself," he said. "I am a young man and I am here looking forward to a happy life."
Stefan is one of the 1,500 asylum seekers and their families currently being looked after by Kent social services. The estimated cost for this year alone is about pounds 3.5m.
"The numbers are constantly rising and the problems that arise keep on changing and increasing," said a tired-looking Peter Brown, leader of the county council's asylum seekers team.
"Basically we need clearer indications from the Government over what they are going to do about this and when they are going to do it."
Certainly, some local residents are far from happy with the situation.
"I makes my blood boil, it really does," said one woman out walking her dog on the country park next to the centre. "We've only just got rid of the gypsies on this park and they were here for 14 years. And now we've got this lot."
Another woman seemed to think this might be a solution to the current problem: "Why don't they put them in tents on the park?" she asked.