Last year the authorities learned of 946 victims, compared with 710 in 2010, the inter-departmental ministerial group on human trafficking said.
It said organised gangs in China, Vietnam, Nigeria and eastern Europe now posed the greatest threat to the UK.
The government said better co-ordination between its departments and with authorities abroad was key.
There is currently no official figure for the number of victims trafficked into the country each year.
However, the group’s report said that last year nearly 1,000 victims were reported to the National Referral Mechanism, the official body that identifies and looks after those caught up in trafficking. Of these, 712 were adults and 234 were children.
Of the victims referred in 2010, 524 were adults and 186 were children. It is thought the increase could be explained by improvements in identifying victims.
The report detailed two cases of people being trafficked for illegal organ donations but they were detected and stopped before the donations were carried out. One involved the planned sale of a victim’s kidneys.
The report also said there had been an increase in the number of children being forced into crime, including street begging. The Child Exploitation and Online Protection Centre estimates there are about 300 child trafficking victims in the UK every year.
Det Insp Kevin Hyland, of London’s Metropolitan Police – which sees the UK’s highest rates of trafficking – said some victims travelled to the UK in lorries or containers but the majority arrived lawfully, often accompanied by their traffickers.
“The vast majority of them think they’re coming to a better life in the UK,” he said.
Mr Hyland said it was often “almost impossible” for border guards to spot victims because they often did not even know they were being trafficked.
Many victims are promised jobs in the hotel or leisure industry, or as interpreters, but when they arrive they are “groomed or threatened”, he said.
Once in the UK they are “moved on to the exploiters” to be used for sexual exploitation or forced labour, or both, he said.
In London, police deal with more than 100 cases of trafficking a year. Some will involve more than 400 victims but the majority involve about 10 to 15 people.
The group’s report said that by far the largest number of referrals of potential victims of trafficking were Nigerian nationals. The largest number of referrals of victims from within Europe involved Romanian nationals.
There are an estimated 92 organised crime groups in the UK known to have an involvement in human trafficking, it said.
And 142 defendants were charged with offences related to human trafficking in 2011/12.
The report said intelligence sharing with international police forces was already “proving effective”.
‘No magic bullet’
Thousands of “front-line” workers, including border staff, police and healthcare workers, have been trained to better identify, support and protect victims over the past two years, it said.
Some airlines, including Virgin Atlantic and Thomas Cook, are also training cabin crew to identify those who engaged in trafficking and their potential victims.
And a 24-hour confidential line has been set up for crew to report concerns to border officials before a plane lands in the UK.
Immigration Minister Mark Harper said trafficking was a “sizeable problem” worldwide, with about 21m people either falling victim to sexual assault or being forced into labour.
Mr Harper said there was no “single magic bullet” to tackle the problem but the key was “cross-government and cross-agency working”.
He said it was vital to work with source countries to stop people being trafficked in the first place but it was also important to look at the demand for trafficked people “and how we cut down on that”.
There had been some success with stopping people at the borders, for example by training staff to spot signs of people being trafficked, he said.