A 14-year-old schoolgirl murdered by a Latvian convicted killer wrote a pro-European Union (EU) essay arguing that barring foreign criminals from entering the country was “racist” just four months before her death, it has emerged.

Her parents, who support the free movement of people, have released the essay as they oppose their daughter’s murder being used to highlight the dangers of unregulated immigration.

Alice Gross was walking along a tow-path by the River Brent in west London on August 28 2014 when she was spotted by Arnis Zalkalns, a 41 year old Latvian. Three hours later Zalkalns was picked up by CCTV calmly buying a can of beer in a local shop. In the intervening hours, Zalkalns had crushed Alice to death by apparently lying on top of her during an attempted sex attack, hiding her body in the river.

Zalkalns, who had served seven years for battering his wife to death in his native country, hanged himself days after Alice’s body was found. But questions were raised over why he had been allowed into the country in the first place, and how his conviction had been missed even after he was questioned about an earlier sexual assault on a girl in London.

The murder was just one example used by Leave campaigners during the EU referendum to highlight the fact that the EU’s rules on free movement of people has allowed foreign criminals a free pass into Britain, where they effectively get to wipe the slate clean.

But Alice’s parents have now released an essay written by the schoolgirl months before her murder, which supported the right of free movement among member states.

“Personally, I believe that the United Kingdom should remain a member of the EU as it allows our country to be considered a communal and friendly country,” Alice wrote in May 2014.

And discussing UKIP’s policy of wanting to bar foreign criminals the right of entry, she wrote: “They believe that this will keep Britain safe from crime by eliminating the number of criminals living in its premises. However, I believe that this takes away the concept of equality amongst the community by implying that criminals don’t deserve the same rights everyone else has. It also depicts Britain to believe foreign criminals are different and dangerous compared to the British criminals, reintroducing the idea of racism.”

She continued: “It reflects on the good of our country, not only showing the strength and stability of our nation but the trust and cooperation we have to make our world successful, which in turn earns the respect of others.

“Although there are some disadvantages that result in our country having slightly less power over its citizens, but what is power over loyalty and alliance amongst a civilised and peaceful union?”

Alice’s parents, Jose Gross and Rosalind Hodgekiss, have told The Guardian that they have chosen to release the essay as they are horrified at the way their daughter’s murder has been used to argue for a regulated immigration system.

They have called for more background checks on immigrants to take place, but are unequivocal in their support for free movement and the EU.

“What we’re talking about and what we’re asking for is a very targeted and proportionate sharing of information about violent offenders,” Ms. Hodgkiss said. “We’re talking about a very small group of people. When that is seized upon to make an argument against all freedom of movement and all immigrants, it’s really dangerous. It tars people with the same brush. It’s a racist agenda.”

Mr. Gross is ardently pro-free movement of people as his father was a Jewish Ukranian who fled to the UK during the Second World War. Despite his daughter’s violent death, he maintains that any attempts to bring an end to free movement is racist.

“Because of his beliefs and who he was – because he was Jewish – in order to survive he had to come to this country,” Mr. Gross said. “They came to get away from racist persecution and not being allowed to express their own thoughts and beliefs. So when the idea of racist causes using my daughter to promote their … It made me practically physically sick.”

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