Three men have been arrested in Dubai on suspicion of kidnapping a British-Iranian businessman, Abbas Yazdi, who disappeared from the Gulf state in June 2013.

The suspects are alleged to be Iranian nationals who recently returned to the United Arab Emirates to clean up the scene of their crime.

The abduction of Yazdi, 44, has raised awkward questions about British legal co-operation with Iranian prosecutors at a time when the two countries had no diplomatic relations. Yazdi's disappearance was raised by the foreign secretary, William Hague, with his then counterpart in Iran, Ali Akbar Salehi.

Yazdi's wife, Atena, has accused the UK's Serious Fraud Office (SFO) of providing Iranian prosecutors with detailed personal information about her husband, including the address from which she believes he was abducted on 25 June.

Iran's state general inspection organisation, which was investigating Yazdi over bribery claims involving the Norwegian oil giant Statoil, had written to the SFO to obtain information about him in February 2013.

The case has also been taken up by the shadow attorney general, Emily Thornberry MP, who is seeking information about the SFO's co-operation and is to raise Yazdi's disappearance in the Commons.

In a letter to the attorney general, Dominic Grieve QC, she wrote: "What are the rules governing interactions between UK prosecutors and their counterparts in countries where diplomatic ties have been renounced? Was co-operation between the SFO and the Iranian authorities a regular occurrence during the period that ties were broken? Has the SFO, or the Crown Prosecution Service for that matter, recently assisted any other regimes that the UK government does not recognise and/or that practise or are suspected of practising extrajudicial execution?"

Atena Yazdi believes her husband is still alive despite initial reports from the Foreign Office that he had been killed during the kidnapping.

She told the Guardian: "I am extremely happy about the news of these arrests. It made me and our children so happy that the investigation is going at least one step forward. We now look forward to hearing any information that these detainees could provide on where Abbas has been taken and what have they done to him.

"We also hope that the UK government engages more in this case and negotiates with Iran about Abbas. We have no doubt that the people who have been arrested had direct involvement in Abbas's disappearance."

The Dubai government press office issued a statement late on Thursday saying its security service had arrested the three men on suspicion of kidnapping Yazdi, who owns a general trading company in the emirate.

"The security apparatus identified the group members and … was able to uncover the method they had used to kidnap the suspect," the statement said.

It quoted Dhahi Khalfan, Dubai's deputy chairman of police and general security, as saying that the three were about to dispose of Yazdi's personal effects when they were arrested. The three were being questioned to find out Yazdi's whereabouts, it said.

A Foreign Office spokesperson said: "We welcome the arrests of three men by the Emirati authorities in connection with the alleged kidnapping of British-Iranian national Abbas Yazdi. The UK will continue to liaise closely with the Emirati authorities on the investigation."

Yazdi, who holds both British and Iranian citizenship, moved to Dubai around 10 years ago.

Iran's foreign ministry has vehemently denied reports that the country has had any role in Yazdi's disappearance.

Responding to allegations that the SFO passed on Yazdi's address to the Iranians, the SFO has said: "We do not comment on mutual legal assistance."