The six men and one woman deny servitude and forced labour charges, at Luton Crown Court.
Police found men living in squalor at the Green Acres caravan park in Bedfordshire last September.
The Connors controlled and exploited the homeless people, making large amounts of money, prosecutors claim.
The seven each deny charges of conspiring to hold a person in servitude and conspiracy to require a person to perform forced or compulsory labour.
The charges relate to eight alleged victims.
The accused are: James John Connors (Big Jim), 34; Johnny Connors, 28; Tommy Connors (Junior), 26; James (Jimmy) Connors, 24; Patrick Connors, 20; Josie Connors, 30; and Tommy Connors (senior), 52.
When police raided the caravan park they found 13 male workers who were not part of the extended Connors family.
Victims were recruited from homeless centres, soup kitchens or simply off the streets and made to carry out daily physical labour, the court was told.
One of the workers told police he saw the site as "like a concentration camp", the trial heard.
The alleged victim, who cannot be named for legal reasons, was living on benefits in Brighton when he was recruited from a day centre by Tommy Connors Snr and two of his sons, it was claimed.
The Connors offered him a job, Â£50 in cash and a roof over his head and took him to a site in Burgess Hill, West Sussex, where Tommy Connors Snr was living, it is alleged.
Prosecutor Frances Oldham QC said: "At first he had been treated OK and given pocket money to buy cigarettes, biscuits and crisps.
"After a while the travellers' treatment of (him) changed. Tommy Snr would hit him in the face for no reason when in a temper."
Some days he was given "no food at all", or just biscuits and crisps to snack on, the court heard.
The labourers were not allowed to leave work to get something to eat, it was alleged.
The Connors are alleged to have coerced their labourers into working for their block paving business for up to 19 hours a day, six days a week.
Sundays were left free for further work by way of door-to-door selling, prosecutors said.
Ms Oldham said: "Men were targeted because they were vulnerable, and kept on sites like camps under orders not to leave.
"Their heads were shaved. They were paid little or nothing for their work. They were on occasions verbally abused and on occasions beaten.
"They may not in the strict sense have been slaves but they were not free men.
"The evidence suggests that the Connors family made very substantial amounts of money through the exploitation of the servitude and forced labour of their workers."
Most of the workers managed to escape at some point but were afraid of being "recaptured", the court heard.
Another alleged victim told police he had suffered "seven years of abuse, starvation and torture," the court heard.
"There was no respect," he claimed. "They treated me like a slave, and that's putting it mildly."
Ms Oldham told the court the man had thought of leaving "hundreds of times" but when other workers went missing he feared they might have been given "a real good pasting".
"There had been times when he could have contacted the police, but he knew that if he got into a police car he would have been 'killed'," Ms Oldham said.
The jury was told the area where the workers slept was "freezing cold", and they were at times given food so old that "flies were crawling over it".
The labourers were taken for showers at most once a week but sometimes only every few months, she said.
Ms Oldham said the first alleged victim never attempted to leave as he was "too frightened to do so".
Some of the workers, particularly those whose captivity spanned many years, appeared to have effectively lost the will to resist, she said.
Some became "conditioned" to do what the Connors family wanted them to do, she added.
"In respect of some of these 'long term' workers, it is clear they collaborated with members of the Connors family in oppressing others recruited," she said.
The alleged crimes came to light when police raided the Green Acres site on 11 September last year.
They had received statements from some men who had "escaped" and officers had been "conducting observations" over a period of time, jurors were told.
The labourers were taken by police to a nearby reception centre where they received medical assessment and treatment, prosecutors said.
The trial continues.
Seven people from one traveller family abused and beat vulnerable men who were kept in captivity and made to work without pay, a court has heard.