The family of teenager Alice Gross, who was abducted and murdered by a recent migrant to Britain driven by a sexual motive, have said they do not want their daughter’s death exploited by anti-immigration groups.

In a statement to the Guardian through their lawyer on Tuesday, the Gross family said they wanted an inquest into the death to consider whether her killer should have been allowed into Britain despite having a previous murder conviction.

But they stressed they did not want to give anti-immigration groups the chance to hijack their daughter’s case.

Earlier on Tuesday, Scotland Yard outlined the evidence it said showed Arnis Zalkalns, a builder from Latvia, killed 14-year-old Alice last August for a sexual motive before weighing down her body on a river bed in west London. Zalkalns then took his own life.

It emerged that he had been allowed into Britain in 2007 despite a previous conviction in Latvia for murdering his wife and concealing her body.

Alice Gross disappeared after going for a walk in west London in August 2014. Photograph: Metropolitan police/PA

Alice’s parents have asked civil rights group Liberty to represent them at the forthcoming inquest.

They said they and their daughter believed in the “free movement” of people across borders and did not want the nightmare they suffered “hijacked by groups with an anti-immigration agenda”.

The family from west London stressed they believed in human rights. Despite their suffering and loss, they are determined to stick by their principles.

Emma Norton, legal officer for Liberty, said the family believed part of the European convention on human rights should help them to get answers to questions they have.

She said: “Liberty has made representations to the coroner that the inquest into Alice’s death must be an Article 2 inquest – that is, an inquest that will look not only into the cause of her death, but also into the wider circumstances.

“In particular, the family wants to know what the authorities knew or ought to have known about Zalkalns when he travelled to the UK from Latvia.

“The family is aware that this is a sensitive and difficult subject, and is concerned to ensure that it is not hijacked by groups with an anti-immigration agenda.

“The family believe in freedom of movement and human rights. That is why they approached Liberty and asked us to help them.

“We hope the coroner will agree that there are important questions that need to be answered, and we are waiting to hear from him.”

The inquest has been opened and adjourned, and no date has yet been fixed for it to be resumed.

Zalkalns stabbed his wife in remote woodland and buried her in a shallow grave. He came to Britain in 2007, having served his sentence in Latvia.

The body of Arnis Zalkalns was discovered in a ‘densely overgrown area’ of Boston Manor Park in west London. Photograph: Rex Features

In 2009, he was arrested over an alleged indecent assault of a 14-year-old girl in west London. That case was dropped after the girl declined to make a statement.

He avoided facing justice for Alice’s death by killing himself and his body was found by police days after they had recovered the girl’s body following a wide-ranging search lasting weeks.

Scotland Yard on Tuesday said there was enough evidence to have charged Zalkalns had he lived and the probable motive for his crime was sexual.

Alice was last seen on 28 August, 2014, after going for a walk. Police believe Zalkalns came across Alice during her final walk along a canal towpath.

One week later, Zalkalns, 41, was reported missing from his west London home.

After a month of searches, Alice’s body was recovered from the Brent river on 30 September, after it had been deliberately weighted down by parts of a tree trunk.

On Tuesday the head of the inquiry, DCI Andy Chalmers, said the “most likely motive was sexual’’.

Scotland Yard set out its case against Zalkalns and its most definitive account so far about how Alice died.

Chalmers said a well preserved cigarette butt bearing traces of Zalkalns’s DNA was found close to where Alice was discovered.

Her body was found wrapped in bin bags, which had been weighed down with a bike wheel and six sections of a tree trunk in a pyramid formation, he said.

An iPhone cover was found in Zalkalns’s garden which has been identified as belonging to Alice by her sister, the detective said.

Chalmers added that there was “no evidence” that a sexual assault had taken place.

On 4 October, Zalkalns’s body was found hanging from a tree in dense woodland in Boston Manor Park, west London.

Police were criticised for the length of time it took to find Alice’s body. On Tuesday they said she was probably killed a few hours after she disappeared.

Alice’s family said: ”It remains impossible to describe the pain of losing Alice. Her death has left a hole in our lives that can never be filled.

“Every day is full of reminders of her life and her loss, and it is hard to imagine a future in which we can find peace or healing.

“Her brutal murder remains shocking, an appallingly senseless act that is still difficult to believe or understand.”

They added: “We would like to thank the local community. Hanwell is a multicultural and multifaith area. The search and grief for Alice united the whole community in an extraordinary display of sympathy and compassion, and this has continued. We are very grateful.”

Zalkalns is believed to have children in Latvia and also to have fathered a child, now aged one, with a woman in London.

A music fund set up in Alice’s name, Alice’s Youth Music Memorial Fund, said it had already received £17,000 in donations.