Relatives of two British sisters-in-law and a baby girl who were killed in a crash in Iceland have spoken of their deep sadness over the incident, in which four other members of the same family were injured.

Rajshree Laturia and Khushboo Laturia, both in their 30s, and the baby, who has yet to be named, died when their 4x4 plunged off a bridge during a family holiday.

They were travelling with their husbands, who were critically injured and airlifted to hospital along with two children, aged seven and nine, after the Toyota Land Cruiser crashed through a railing on a single-lane bridge in southern Iceland before sunrise on Thursday, and fell eight metres on to a sandy riverbank.

Rajshree and Khushboo Laturia, British citizens of Indian descent, lived in London with their families. An official at the Indian embassy in Iceland said he was unable to confirm their names officially, but that he understood they were the identities of the deceased.

Their family said in a statement: “The fatal car crash near Skaftafell in Iceland on the morning of December 27, 2018 has come as a horrifying shock for the entire family and friends.

“The Indian, British and Icelandic authorities have been extremely cooperative and extended appropriate support. Our family is deeply saddened so we request you to kindly respect our privacy and give us the space to grieve in peace at this difficult time.

“Special thanks to the local authorities for airlifting and ensuring timely medical facilities were provided. Thank you for your prayers and understanding on this matter.”

The women were travelling in the rented vehicle with Shreeraj Laturia, married to Rajshree, and his brother Supreme Laturia, married to Khushboo. Armstrong Changsan, the Indian ambassador in Reykjavik, visited the survivors in hospital on Thursday.

Shreeraj and Rajshree Laturia, who both worked in finance, were included on a list of Asian power couples in 2015. Rajshree worked at Barclays Capital for three years until 2009 as an assistant vice-president before joining Morgan Stanley, according to a citation on the Asian Power Couples website, which has since been removed.

Shreeraj is said to have had a “successful track record in trading and financing structured credit product portfolios”. According to his LinkedIn page, he spent eight years at UBS Investment Bank as a portfolio manager and trader from 2006 until 2014. He joined RBC Capital Markets as a trader in 2015.

Another brother, Sarvesh Laturia, told the Times of India: “It was my two brothers and their wives, they are British people. They were on vacation in Iceland and their car met with an accident in which my two sister-in-laws passed away and my niece passed away. My two brothers are in a critical condition in hospital.”

The crash took place on a ring road between the town of Kirkjubæjarklaustur and Skaftafell, part of Vatnajökull national park. Police have launched an investigation.

Adolf Erlingsson, a tour guide who was among the first on the scene, suggested the driver lost control of the car. “It was horrible. The car seemed to have hit the ground many metres from where it stopped. We struggled getting everyone out,” he said.

Local police said on Friday: “The individuals involved in a traffic accident at Núpsvötn yesterday are all British citizens. The individuals were two brothers travelling around Iceland with their families. The deceased were two women born in 1979 and 1980 and an infant born in 2018.

“The cause of the accident is unknown and under investigation by the police and the investigative committee for transport accidents. It is clear that the car was driven past the cameras at Hvolsvöllur early that same morning.

“The car was driven to the east, along the Sudurlandsvegur road, and seems to have turned on the bridge with the result that it went on top of the railing of the bridge, to the right, following it for a short distance and then turned over off the rail and the bridge. There, the car fell down on the ground beneath the bridge.”

The bridge was built in 1973 and is one of the longest in the country. It was not thought to have been icy but police said humidity may have made its steel surface slippy.