The Foreign Office is helping a British family of seven who were arrested in the US and subject to the “scariest experience” of their lives at the hands of the immigration authorities after inadvertently crossing the border from Canada.

David and Eileen Connors and their three-month-old son were on a family road trip on 3 October near Vancouver with David’s cousin Michael, his wife Grace, and their two-year-old twin daughters.

All seven members of the London family were arrested when Michael, who was driving, took a detour to avoid an animal in the road and crossed into the US without realising it. They remain in detention awaiting deportation to the UK amid fears for the welfare of the three children involved.

Since the family were arrested they have been subjected to an ordeal that Eileen said would leave them “traumatised for the rest of our lives”. She made the comments in a statement that forms part of a legal complaint against the US Department of Homeland Security about their treatment.

In a statement, the Foreign Office said: “We are providing assistance to a British family after they were taken into custody in the US and are in close contact with US Immigration and Customs Enforcement.”

Eileen Connors’ statement was released by her lawyer, Bridget Cambria, from Aldea – the People Justice Center – an organisation that provides legal help to immigrant families to the US.

An email to the Guardian from an unnamed staff member at Aldea said the case exposed the poor treatment facing many migrant families in the US.

The email said: “While we are conscious of the extreme vulnerability of this child due to his young age, we would take this opportunity to highlight that there are approximately eight children under the age of five, half of them two years of age or under (including the British citizens), in a facility that is not licensed by the state to hold children.”

US Immigration and Customs Enforcement (Ice) insisted that the Connors were being held in “a safe and humane environment for families”. In a statement to the Guardian it said it was “unequivocally false” to suggest that conditions were inhumane.

In her statement, published by the Philadephia Inquirer, Eileen said the US police ignored protestation of innocence and ignorance of crossing the border. After they were arrested, David and Michael were separated from their wives and children, it said. For the first night Eileen was held with her baby in a women’s cell with only foil blanket to keep warm, the statement claims.

Despite being told they would be released to a family member in the US, David, Eileen and their son were then taken to a detention centre in a journey she likened to “an abduction or kidnapping”. David was then held in the centre while she and the baby were put up in a hotel in Seattle. Eileen’s statement only describes her treatment and that of her husband and son.

But it is understood that all seven of the family were flown 2,400 miles from Seattle airport to Pennsylvania on 5 October and taken to the Berks county residential center, one of three places in the US used to hold migrant families. Campaigners, including Aldea, the organisation now representing Eileen, have labelled it a “baby jail” which they say is not fit to hold children.

In her statement Eileen complained about the cold and filthy conditions at the centre where she and her baby were given bedding that smelled “like a dead dog”. She said her baby boy’s eye became swollen and his skin blotchy while in the centre. She was also told she could be separated from her baby.

Her statement said: “We have been treated like criminals here, stripped of our rights and lied to … We will be traumatised for the rest of our lives by what the US government has done to us.”