More border police are needed to tackle "highly sophisticated" trafficking gangs targeting the UK, a think tank has warned.
A report from the Centre for Social Justice claims the gangs are several steps ahead of the authorities.
BBC News has visited one Slovakian village where homes are alleged to have been built with trafficking profits.
The government said recent legal changes would make it harder for people to be exploited in the UK.
But Fiona Cunningham, a former Home Office adviser and author of the Centre for Social Justice report, told BBC News that the "organised criminality that lies behind this modern form of slavery is pretty much endemic now".
The report calls on the government to increase cross-border police operations in order to tackle the problem.
Though the government estimates there are around 13,000 trafficking victims in the UK, experts said the figure was conservative.
The European Union's (EU) open borders policy has facilitated many opportunities for trafficking people.
Ms Cunningham said: "Organised crime groups find the trafficking of victims to be a highly lucrative and accessible crime to pursue and as such have become highly sophisticated in developing illegal business models."
In Slovakia, most of the 170 trafficking victims that have received support in recent years have been exploited in the UK.
"The forms of trafficking are combined," said Anna Bartosova from the Catholic charity Caritas, which works with victims in Slovakia.
"They force them to work and they use their documents for benefit fraud."
'Capital of human trafficking'
Since the UK opened its borders to people from EU accession countries in 2004, hundreds of people have moved to Britain from the small village of Pavlovce nad Uhom in eastern Slovakia.
Most of the villagers, who are overwhelmingly Roma, came here to work.
But BBC News has been told that some have since become engaged in trafficking people to the UK, or exploiting individuals when they are already in Britain.
Local social worker Yves Ogou told the BBC: "Pavlovce is the capital city of human trafficking in eastern Slovakia."
The village has been transformed in recent years by the money made in the UK by villagers.
Two storey, multi-coloured brick homes, some with CCTV cameras, are replacing the small wooden or concrete shacks that people used to live in.
While most have been built with money legally acquired, Mr Ogou says a few have been built with the proceeds of human trafficking.
Some criminals have engaged in fraud, taking people to the UK, stripping them of their documents and claiming child benefit for children that do not exist or that are not their own.
"It's stupid, unbelievable," said Mr Ogou. "Within one minute you can check if the guy has a kid here or not. And you don't."
A few miles away from Pavlovce, in a small village, we found two families whose daughters are living in England, married to Pakistani men.
Though both said the marriages were legitimate, a man from the village was convicted in Manchester last month of arranging sham marriages.
One local told me he had heard the going rate for marrying a Pakistani man - allowing the groom to gain access to an EU passport - was "between 2,000 and 3,000 Euros".
Legal loopholes in the registration of marriages in Britain have previously allowed the marriages to take place, according to experts.
The report highlights how the internet has made it easier to entice and control people, with criminals at times using webcams to monitor their victims.
'They beat me'
But word of mouth is still a prevalent recruitment tool. One victim was enticed to come to Britain after talking to a man who promised him work.
Within days of arriving here, his documents had been taken from him, the first step in eight years of beatings and exploitation as he was forced to travel the country - working first for Slovak and then Irish Roma gangs.
"Every day they beat me, broke my leg, my ribs, my nose," said the man, who does not want to be identified. "All the money went to them, nothing for me."
Last month, police raided properties in Berkshire, London and Yorkshire as part of a clampdown on human trafficking.
Officers made arrests and recovered victims after an 18-month investigation known as Operation Rehoboam.
On Tuesday, four Slovakians were arrested in Newcastle as part of a nationwide operation tackling human trafficking.
In recent days, EU ministers have met in Luxembourg to discuss the ongoing migration crisis in the Mediterranean.
Several hundred people are feared to have drowned over the weekend, after their boat capsized.
On Monday, the EU's head of foreign affairs, Federica Mogherini, said the EU had finally woken up to the evil of human trafficking.
The European Commission has come up with plans to try to deal with the crisis - including increasing the size of Europe's naval operations in the Mediterranean.
Speaking ahead of the talks, UK Foreign Secretary Philip Hammond said a "comprehensive, European-level response" was needed in order to target the criminals "managing this traffic in human suffering".
But with open borders, online technology and sophisticated networks, the criminals will continue to pursue new victims.