It's calling for the authorities here in Britain to close a loophole which it says has allowed child trafficking to become the fastest-growing area of organised crime.
Breakfast talked live to UNICEF's special representative, Jemima Khan, who has talked to some of the young victims of global child trafficking.
"It's impossible to describe the trauma that they have been through," she told Breakfast this morning.
"Many have been beaten and raped, persecuted, incarcerated in their homes, forced to work long hours, deprived of education and deprived of their basic human rigths.
"Typically, the children are led to believe that they will get a better life - and that's why they go with the traffickers."
Unicef believes around 1.2m children are trafficked across the world each year - and hundreds, or possibly thousands of those children arrive here in the UK.
"There is a legal loophole," Jemima explained "which means that it's not illegal to traffic a child, except for the sex trade." So, for example, it was perfeclty legal for Victoria Climbie's aunt to bring her into Britain, to obtain benefits.
Unicef wants better training for immigration officers, who may be the only British officials who come into contact with victims of child trafficking.
It also wants children who have been trafficked to be allowed six months' grace by the authorities, during which time they can decide whether to go home or to stay in Britain and help prosecute those responsible.
Further details from BBC News Online
The children are being drawn from a growing number of countries - mainly from West Africa, but also from other African countries, Eastern Europe, Asia and even Jamaica.
The issue hit the headlines on Tuesday when 21 people were arrested in the case of 'Adam', the Nigerian boy whose torso was found in the river Thames in 2001.
Police believe a ring of people trafficked the boy into Britain before he was ritually killed.
Trafficking is often being masked by the West African cultural practice of sending children to live with extended family or friends to be educated or to find work, said Unicef.
Between 8,000 and 10,000 children are being privately fostered in the UK, it said - many from West Africa.
This was often for the child's benefit, but "many of these children could be being abused or exploited, without anyone even knowing they are in the country," it said.
Another West African child, Victoria Climbie from Ivory Coast, was tortured to death in 2000 by a London-based great-aunt who used her to claim child benefits.
Towns and cities
Children are now being taken not only to London and other UK capitals, but to smaller towns and cities nationwide where the authorites may be less aware of the problem, said Unicef.
"In some cities such as Nottingham and Newcastle, cases have only started coming to light since late 2002, indicating that the traffickers are widening their operations and trying new places," it said.
Unicef said the children were controlled and intimidated in a number of ways - with Albanian gangs using rape, violence and threats against relatives, and West African traffickers threatening voodoo and curses, for instance.
Escaped from abusive father in Romania aged 12
Asked family friend for help: He took her to Serbia and sold her
She was prostituted there and then in Macedonia, Albania, and Italy
Resold and brought to the UK, again for prostitution
Escaped into social services' care
Her trafficker sentenced to 10 years in prison in 2002
"It's a huge concern for us, not least because of the terrible, appalling suffering which the victims go through," said Unicef UK's executive director David Bull.
"You can imagine almost nothing worse than being forced or tricked away from your family to a foreign country where you're abused and beaten and sexually sold almost on a daily basis."
The Sexual Offences Bill, currently in the House of Commons, will make it illegal to traffic people into the UK for commercial sexual exploitation.
But children trafficked for other reasons will remain unprotected.
Unicef called on the government to criminalise trafficking for all purposes.
WHAT IS CHILD TRAFFICKING?
Trafficking means transporting and exploiting unwilling or unknowing victims
Child victims often used for sex work
May also be used as domestic servants, drug mules, in sweatshops and restaurants, or as beggars or pickpockets
It also urged the government to provide funding for specialist care - including safe house accommodation and counselling for the victims, and training for immigration officers and social workers.