Around 5,000 have vanished in Italy alone, with a further 1,000 unaccounted for in Sweden, Europol's chief of staff Brian Donald has said, The Independent reported.

It is feared many have become victims of exploitation by criminal organizations, particularly as gangs established in human trafficking are now known by Europol to be engaging refugees in sex work and slavery.

"An entire [criminal] infrastructure has developed over the past 18 months around exploiting the migrant flow," Mr Donald told the Observer.

Ninety per cent of refugees have paid a criminal gang to reach Europe, making last year one of the most profitable to date for human traffickers, Europol recently told The Independent on Sunday.

At least 340 children are known to have disappeared in the UK since registering as asylum seekers between January and September 2015, with double the number disappearing in 2015 than in 2014.

"It's not unreasonable to say that we're looking at 10,000-plus children" who are unaccounted for in Europe, said Mr Donald.

"Not all of them will be criminally exploited; some might have been passed on to family members. We just don't know where they are, what they're doing or whom they are with."

Europol estimates 270,000 child refugees arrived in Europe last year, more than a quarter of the 1.1 million refugees who arrived in total. According to Save the Children, 26,000 of these children were unaccompanied.

The intelligence agency has evidence child refugees have been sexually exploited in Europe.

"These kids are in the community - if they're being abused it's in the community. They're not being spirited away and held in the middle of forests, though I suspect some might be. They're in the community – they're visible. As a population we need to be alert to this," Mr Donald said.

The figures come as David Cameron refused calls to resettle 3,000 unaccompanied child refugees living unaccompanied in Europe.

The Home Office has confirmed it will bring more unaccompanied children to the UK from Syria and other conflict zones, but will not accept children who have already arrived in Europe.

Doing so would encourage more children "to make the difficult, potentially lethal, journey to Europe”, Cameron told Sky News.

Immigration minister James Brokenshire said the "vast majority" of refugees were "better served staying in the region so they can be reunited with surviving family members."