The Qatari organisation in charge of staging the 2022 World Cup has agreed to hold a wide-ranging inquiry led by a British judge into the death of a British worker during construction of a stadium for the event.

The decision, two-and-a-half years after the death of Zac Cox in January 2017, is seen as a breakthrough for campaigners disturbed by health and safety issues surrounding the building of the stadiums, even though it comes relatively close to the completion of the bulk of the construction work for the tournament.

Campaigners said it was the first known inquiry into a specific death during the construction of World Cup stadiums. The inquiry will be conducted by Sir Robert Akenhead, a former high court judge with expertise in construction law and site accidents.

In February 2018 a British coroner sharply criticised safety measures at the stadium site. She said equipment provided to Cox was not fit for purpose.

Cox’s two sisters-in-law, Ella Joseph and Hazel Mayes, said in a statement that the period since his death had been “extremely difficult for the family” and they were pleased by the decision from the Qatar Supreme Committee for Delivery and Legacy.

They said: “We wanted to get to the truth about the decisions and circumstances that led to his death and to try to ensure that lessons are learned that could prevent other similar accidents occurring in the future.”

According to the statement, Akenhead has been asked to “examine the underlying causes of Zac’s death, the decisions that led to the death, the process of investigation since the death and safety lessons that have been learned and enforced since the incident”.

The family said they also welcomed a commitment from the Qatari committee to ensure that “everyone concerned cooperates fully with this independent investigation”. They said Akenhead should be allowed to carry out his work with “complete autonomy”.

The long gap between Cox’s death and the establishment of the inquiry underlines the sensitivity of the issue in Qatar and the persistence of the family in seeking fuller answers as to how he died.

Cox was killed at the Khalifa International Stadium after falling 40 metres off a suspended platform. He was employed by a South African subcontractor working for a German firm.

The accident occurred after lever hoist equipment failed, causing part of the platform on which Cox and a colleague were working to fall.

The coroner in Cox’s inquest, Veronica Hamilton-Deeley, said: “Many managers knew and should have known they were effectively requiring a group of their workers to rely on potentially lethal equipment.”

She said changes introduced to speed up the installation of the catwalks were “chaotic, unprofessional, unthinking and downright dangerous”.

Hamilton-Deeley said “a perfect storm of events” led to Cox’s death, including a decision by the contractors to speed up the building of the stadium’s roof. That move required the use of additional lever hoists that a fellow construction worker told the inquest were worthy only of the rubbish bin.

One crucial piece of information eventually submitted to the inquest was an internal report prepared by the contractors but never formally given to the family. The family obtained the report through unofficial channels and it said lever hoists used by the contractors did not have up-to-date safety certificates and that the health and safety system had not been followed.

Pfeifer, the German contractors working on the site, claimed that the report was not official because it was internal and therefore “not relevant”.

Speaking at the time of the coroner’s inquest, Mayes said the internal report, which was completed within 11 days of the incident, “gives the most factual account of the event”.

In one of the many injustices in the case, one of Cox’s colleagues, Graham Vance, a South African who had been working alongside Cox when he fell, was arrested on the same day and was unable to leave Qatar for 11 months until a police investigation had concluded and he was cleared of any involvement.

“We were initially reluctant to come forward because we had absolutely no desire to create any further pressure on Graham, who we have always believed to have been an innocent victim of this process,” Mayes previously told the Guardian.

She said: “Knowing that he was wrongfully held out there in Qatar for us was deeply distressing. He had just witnessed the death of his colleague at close proximity and it must have been an absolutely awful 11 months for him.”

The Qatari committee said in a statement after the coroner’s verdict last year: “Several systemic failures and human errors contributed to this incident.” It acknowledged its failure to engage with the family directly over the reasons for his death.

The committee added: “We are wholly committed to ensuring Sir Robert Akenhead is able to conduct his activity unhindered and with absolute autonomy and full co-operation. Any lessons that can be learnt from this investigation and applied to our World Cup projects to ensure an incident like this does not occur again will be welcomed.

“The health and safety of all of our workers remains as our utmost priority. We will be making no further statements until the investigation has concluded.”

Qatar’s treatment of migrant workers mainly from south-east Asia has been a source of criticism ever since the small but hugely wealthy nation won the right to stage the World Cup in December 2010.

Probably the most critical account of the safety culture in the stadiums was written by Human Rights Watch in September 2017. It called for regular autopsies into all deaths, and death certificates explaining cause of death. Its author claimed deaths continued at a high rate, although the International Labour Organisation has welcomed changes to mid-day working and exit visas for guest workers.