Young children are being groomed and sexually assaulted and women are afraid of sexual attacks in government-run refugee camps in Greece, according to reports.

One volunteer at the Softex camp on the edge of Thessaloniki told The Observer that a seven-year-old Iraqi girl was attacked by a man from a 'mafia' group operating in the camp.

"A man from one of the 'mafia' groups asked their seven-year-old daughter into their tent to play games on his phone and then zipped up the tent," the volunteer said.

"She came back with marks on her arms and neck. Later the girl described how she was sexually abused. It has scarred a seven-year-old child for life."

The family is now planning to return to Iraq rather than settle in Europe.

Aid groups working in the Softex camp confirmed that they had seen a rise in sexual violence.

"It's really hard for the unaccompanied minors – 16- and 17-year-olds – to survive. It's the survival of the fittest in there. In the evening and night it's impossible to find them [children] because they are hiding in the tents," said Anna Chiara Nava of Médecins Sans Frontières in Thessaloniki.

"The women are afraid. They complain that during the night and evening they cannot go to the toilet alone. They have all heard of reports of others being attacked."

The office of the UN High Commissioner for Refugees admitted sexual violence is "an issue when it comes to Softex and others."

"UNHCR has been raising concerns about this, specifically about this issue [sexual violence], saying that we don't think it will be safe for women and for children," it told The Observer. "We've raised the issue of security again and again. This is a problem; it's under discussion."

The reports follow findings from Unicef that sexual violence and forced prostitution is a constant threat for children in refugee camps in Northern France.

Some young women have exchanged sex for the promise of passage to the UK, researchers said, and children must pay an "entry fee" before they are even allowed to live in the camps. Unaccompanied minors are forced into labour if they can't afford to pay.

Labour MP Yvette Cooper, chairwoman of the refugee taskforce, said the latest allegations should "shame us all".

"The UK government needs to urgently wake up to its responsibility," she added.

Cooper referred to the Dubs amendment passed by MPs earlier this year, under which unaccompanied refugee minors in Europe can now legally be relocated to the UK. "Parliament passed the amendment exactly because we were worried about child refugees being exploited, trafficked and sexually abused because other countries were overwhelmed with the scale of the problem," she said.