Last year the authorities learned of 946 victims, compared with 710 in 2010, the inter-departmental ministerial group on human trafficking said.
Trafficking gangs in China, Vietnam, Nigeria and eastern Europe now pose the biggest threat to the UK , it said.
The government said better co-ordination between its departments and with authorities abroad was key.
But anti-slavery groups warned government "failures" had led to "significant steps back" in the fight.
By Tom SymondsHome Affairs correspondent
In Ilford, East London, the police moved in at 05:15 BST, smashing through the door of an end of terrace house, but without result. It was empty.
The Met says it carries out two such raids every week, on average.
Two miles away in a second house, they found a Lithuanian family living in one room. A stack of mail showed that a large number of people have stayed there before.
They questioned the Lithuanians who said they were being paid below minimum wage to work in a recycling depot and building firm.
The room costs Â£140 a week. There was a CCTV camera watching the door of the house.
Are they victims of people trafficking? It's not clear, and often those involved haven't asked themselves the same question.
But police say those who try to run are often subject to violence.
There is currently no official figure for the number of victims trafficked into the country each year.
However, the report said 712 adult victims and 234 child victims were reported last year to the National Referral Mechanism, the official body that identifies and looks after those caught up in trafficking.
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, although campaigners say the figures of those being trafficked could be far higher as many victims choose not to come forward for fear of being deported.
The report suggested 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.
The report also detailed two cases of people trafficked for illegal organ removals, but they were detected and stopped before the operations were carried out.
One involved the planned sale of a victim's kidneys.
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" and used for sexual exploitation, 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 report revealed the largest number of referrals of potential victims of trafficking were Nigerian nationals. From within Europe, Romanian nationals were the biggest group referred.
There are an estimated 92 organised crime groups in the UK with known involvement in human trafficking, it said.
And 142 defendants were charged with offences related to human trafficking in 2011/12.
By Philippa RoxbyHealth reporter, BBC News
The two potential victims of organ trafficking in the UK in 2011 are the first people identified as being forced into giving up their internal organs for transplant.
But it's still a small problem, with organ trafficking making up only 1% of all potential victims of trafficking last year, according to the Serious Organised Crime Association.
Cases of illegal organ trading are rare in the UK because of safeguards in place.
The Human Tissue Authority sees 1,200 cases a year of living organ donation - 95% involve kidneys and 5% liver lobes.
These cases include people making altruistic organ donations and those coming from abroad to donate organs to family members.
The HTA interviews all potential donors to make sure they are consenting freely and to ensure there is no reward or payment.
The process can take up to six months with the donor required to sign a form stating no coercion was involved.
Only when the HTA is satisfied would the operation be allowed to go ahead.
Advice is being drafted for NHS staff to help them identify potential cases of organ trafficking.
The report concluded intelligence sharing with international police forces was already "proving effective".
Immigration minister Mark Harper said the results demonstrated UK professionals were getting better at "spotting" the crime due to "cross-government" cooperation.
"We're doing a better job of cracking down people involved in the vile trade," he told BBC Radio 5 Live.
But the number of those prosecuted was "not enough," he said.
"One of the things we do is to prosecute people for the most serious offences we can, and sometimes that's not a trafficking offence."
Mr Harper also said agencies needed to "make sure victims who are trafficked are treated as victims and not as offenders, which has happened in the past".
Dr Aidan McQuade, director of Anti-Slavery International, said Mr Harper "must face up to the fact" that the problem was worsening "because of fundamental policy failures".
He said the government viewed the problem "through the lens of immigration" and had allowed rights for migrant workers to slip from "best practice".
"It would be helpful if the government appointed a national commissioner on trafficking to make sure policy on this issue was unimpeded by politics."
The report revealed 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.
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.
The number of people being trafficked into the UK is rising, latest government estimates suggest.