Among genuine jobseekers arriving in the UK each year from other EU states, there are a number of sex and violent offenders who enter undetected.
Dembovskis had raped two other women in Latvia
As Brussels tries to find a way of increasing information-sharing among its 25 members, File on 4 asks if enough is being doing to monitor cross-border criminals?
The programme highlights the case of Josef Zygmunt Kurek, a 40-year-old convicted rapist from Poland who found employment at a plant hire firm in south Wales in 2004.
One night in August 2005, after celebrating the birthday of his boss's wife, a drunken Kurek broke into a woman's house and raped her.
As an employer, the firm had no way of checking if Kurek had a criminal record. While EU citizens can move freely across the union, criminal records don't.
Kurek was jailed for life at Swansea Crown Court in November 2005. The judge described him as a danger to women and said he would have to serve a minimum of five years in prison before he could apply for parole.
Eluned Morgan MEP says while there are benefits to the UK opening its doors to migrant workers from the EU, safeguards were needed to monitor dangerous criminals like Kurek.
"At the very least we should be aware, or the police should be aware, of who is living in our midst and what kind of record they have and whether they should be keeping an eye on them or not," she says.
"That is something we expect of our own citizens and I think we should expect it of people who come to our country as well."
There is currently no requirement for member states to inform their neighbours about convicted criminals travelling abroad.
Such safeguards might have alerted authorities to Viktor Dembovskis, a Latvian who moved to London in 2004, shortly after the country's accession to the EU.
In May 2005, he brutally raped and murdered Jeshma Raithatha in May 2005, as she walked home from school.
He was sentenced to three life sentences for the murder. During the trial it emerged Dembovskis had served two jail sentences for rape in Latvia during the nineties.
The programme speaks to one of his victims, Svetlana Dolbikova, who was 19-years-old when she was raped by Dembovskis in a small town, east of the Latvian capital Riga.
"I think he is the kind of person who will just go on and on...all his life," she says.
But as there is no sex offenders register in Latvia, authorities there have no way of monitoring its sex offenders once they are released from prison.
Brussels recognises the importance for better information-sharing between member states, especially as the union continues to enlarge.
Fourniret continued committing sexual offences in Belgium
It was the case of Michel Fourniret, dubbed the Ogre of the Ardennes, that provided the impetus for action.
Despite convictions for sexual assaults on minors in France, Fourniret was able to move unchecked to Belgium, where he continued committing sexual offences.
He was arrested in 2003. He later admitted to murdering nine people, mostly young women and girls - burying some of them at his home in the Ardennes.
In the wake of the Fourniret case, the Belgians put forward a proposal whereby a sex offender banned from working with children in one member state would automatically be banned from doing so throughout the EU.
But MEP Mr Morgan tells the programme that nothing less than a central European sex offenders register will do.
But there remains major obstacles to overcome, including sovereignty, jurisdiction, IT and language.
File on 4: BBC Radio 4, Tuesday 13 June at 2000 BST, and repeated on Sunday 18 June at 1700 BST. Or listen online - see links on the right hand side of this page.