According to the European police agency Europol, more than 10,000 children who entered Europe during the last two years have disappeared, vanishing through the gaping cracks in Europe’s chaotic system for dealing with refugees and migrants.

The fear is that many of the missing children have been trafficked into the sex trade by the same organized criminal groups that are profiting handsomely by ferrying refugees into and across Europe.

In addition, many children are believed to have fled detention centers, where they do not feel safe and are too often kept in the dark about their rights. Some are teenage boys, many from Syria and Afghanistan, who have been sent ahead by families hoping to join them later.

Once on the streets, they are easy prey for drug dealers, pimps or petty-theft rings. Younger children and adolescent girls are also at great risk of sexual and other abuse.

Some children may have become separated from their families along the routes refugees take through Europe after landing in Greece or Italy. Others arrive in Europe as unaccompanied minors — 26,000 last year — according to the humanitarian group Save the Children.

And more are arriving every day. The United Nations says that more than a third of refugees crossing the Mediterranean by boat to reach Europe are now children. Last year, more than 70 percent of refugees who arrived in Europe were men.

“The implications of this surge in the proportion of children and women on the move are enormous — it means more are at risk at sea, especially now in the winter, and more need protection on land,” warned Marie-Pierre Poirier, UNICEF’s special coordinator for the refugee and migrant crisis in Europe.

Britain’s Department of International Development is setting up a $14 million fund to support refugee and migrant children on the continent. That is helpful, but Britain, which has so far balked at taking any refugees already in Europe, should also take in a fair share of unaccompanied children — as should all other European countries.

The European Union also needs to increase funding to improve services for these children. The trafficking networks must be broken, and any perpetrators of crimes against children must be apprehended and punished.

All European countries have signed the United Nations Convention on the Rights of the Child and have a duty to provide for the safety and well-being of children on European soil. That Europe has failed to protect these most vulnerable among the desperate people arriving on the continent is unconscionable.