A tightening of safety rules in New Zealand’s adventure tourism industry is being demanded by the family of a British traveller killed in a skydiving plane crash.

Parents of 24-year-old Bradley Coker from Farnborough in Hampshire have got together with the grieving families of the three other overseas tourists killed in the crash to write to prime minister John Key calling for changes in the law to improve New Zealand’s safety record.

Their letter follows publication of an inquest report, which found that the unrestrained passengers had moved backwards during take-off, contributing to instability that made the Fletcher FU24 aircraft uncontrollable seconds after lifting off from an airstrip at Fox Glacier in September 2010.

Among the recommendations of the coroner Richard McElrea was a call for passenger restraints to be urgently considered.

But McElrea said: “It is unlikely that the cause of the crash will ever be fully understood.”

The families say they consider an earlier report into the accident and the inquest findings to be “disturbing” and urge Key to “take decisive and unequivocal action to reassure the world that New Zealand is a very safe place to visit”.

Among their requests are the introduction of stricter corporate liability regulations, the Daily Telegraph reported.

Key, who is also the tourism minister, said he is “personally committed” to improving safety and that his government will urgently consider the coroner’s recommendations.

Others who died in the crash were Patrick Byrne, 26, of County Wexford, Ireland, Glen Bourke, 18, from Australia, and Annika Schmidt, 23, from Germany, along with four tandem dive instructors and the pilot.