After Darrell Simester, then 30, went missing on vacation at a south Wales seaside resort in Aug. 2000, his family didn’t see him again for almost 13 years. They never gave up trying to find the “vulnerable” and “timid” Simester — and their perseverance eventually paid off. In March 2013, an anonymous tip-off led Simester’s family to a two-berth caravan in a stable yard just outside Cardiff, Wales’s capital city. There they found him, now aged 43, in dirty, torn clothes and with teeth missing – but otherwise okay.

Simester’s case sparked a major police operation codenamed Operation Imperial. In police raids in September, two other men (one Polish, one British) were also found living in poor conditions at or near the same site where Simester had been found. Three men have subsequently been arrested and released on bail, all charged with false imprisonment, conspiracy to hold a person in servitude and conspiracy to force a person to work. A 42-year-old woman has also been released on bail.

Rather than being an isolated incident, the U.K. Home Office said in a statement that the case serves as an “appalling reminder” of the extent to which slavery has reappeared in the country. A report released on Oct. 17 by the Global Slavery Index says that it is estimated there are as many as 4,000 people enslaved in the U.K. – and that more could be done to help them and others from sharing their fate. While slavery — or human trafficking — is often thought of in terms of female victims of sexual exploitation, the statistics suggest that the gender distribution is relatively even. Of the 2,255 potential human trafficking victims identified in the U.K. in 2012, 40% were male. And in addition to sex, the trade in human beings for financial gain can involve forced labor, domestic servitude and even organ harvesting. In 2012, some 87% of the 507 potential victims of forced labor exploitation in the U.K. were male.

To put human trafficking in its international context, it is the third most profitable business for international organized crime after the drugs and arms trades – and is globally estimated to generate profit margins of billions of dollars per year. As of June 2012, the International Labor Organization estimated that 20.9m people are victims of forced labor and sexual exploitation worldwide. And the 2012 U.N. Global Report on Trafficking in Persons says that men and boys are estimated to account for approximately 25% of trafficking victims detected worldwide. But as the report points out, official statistics represent only the “tip of the iceberg” as criminals generally go to great lengths to conceal their activities.

There has been an increasing awareness of male human trafficking in the U.K. over the last couple of years, propelled by increased police activity in the area and a growing number of victims being identified. In response to this, the Salvation Army carried out a research project on male trafficking victims in the U.K. in Sept. and Oct. 2012. Key findings included 83% of men in the sample being of eastern European origin, 86% being subjected to labor exploitation and 23% reporting sexual exploitation. Many victims were also identified as being “vulnerable.”

“In the case of British nationals, victims of human trafficking often had pre-existing mental health conditions, learning disabilities, or drug and alcohol problems. Many eastern European men come to the U.K. to look for a better life and find themselves in situations different from those they had expected. This is not helped as many have to overcome language barriers and cultural differences which makes it harder for them to understand what is happening to them and how to address problems,” said Gayle Munro, the research manager at the Salvation Army.

Like Simester, 27-year-old Mark Ovenden is a survivor of modern slavery. In an interview with TIME, he recounted how an Irish traveler family offered him accommodation and employment just outside his hometown in southern England. At the time – Sept. 2009 – he had no job and was eating out of soup kitchens, so he jumped at the chance to earn some money. But things did not turn out as Ovenden expected. Between Sept. 2009 and April 2010, he moved with the family to different areas in the U.K., Holland and Sweden where he was forced to work for either no money or minimal pay. The work – taking up and laying driveways – was physical, repetitive and generally involved laboring for long hours. Ovenden, who said he had no support network of friends or family at the time, soon became completely dependent on his bosses.

“I didn’t have any money in my pocket whatsoever, I was hundreds of miles from home and I didn’t think anyone was going to believe me if I told them what was happening,” Ovenden said. “While I was never beaten, I saw other workers being punched, kicked, shoved, attacked with shovels and pickaxes. And when you see that going on you don’t feel as though you can escape – you don’t want to end up as that guy.” But in April 2010, Ovenden did eventually manage to escape by going to the police for help while he was working in Sweden. Afterwards, he admitted it took him a long time to learn to trust people again – but he eventually managed to rebuild his life and is currently working with a number of anti-slavery charities in the U.K.

The two men Ovenden had worked for directly were tried in Sweden but found not guilty on a technicality. Then they returned to the U.K. where they “carried on where they left off,” says Ovenden – and both were arrested in 2011 on charges of conspiracy to hold a person in servitude, along with several other members of their family. Five family members – including one of Ovenden’s previous bosses – were convicted and sentenced to up to six-and-a-half years in prison. But while justice was meted out in this case, the number of convictions for trafficking crimes across the world is low and all too often traffickers fail to be brought to justice for their actions. “For traffickers the profits are very high and the risks are fairly low,” says Tara Topteagarden, the trafficked boys and young men’s adviser at the U.K. Refugee Council.

That said, progress is being made: some 15 people were charged with the offense of forced labor and servitude between 2011-12 in the U.K. (compared with no charges for this crime in previous years) and the U.K. government is currently in the process of drafting a modern slavery bill. But while individuals like Simester and Ovenden are very much survivors, there are many more male trafficking victims whose tales are not being told. “National data on victims of trafficking shows only those who have been picked up and identified by the system. We know there are many more people who fall through the gaps,” says Topteagarden.