A Saudi court condemned the 15 Saudi Shias to death on Wednesday after finding them guilty of spying for Iran.
Tehran swiftly denied the espionage charges and urged Saudi Arabia not to "seek to bring baseless accusations against Iran with the intention of political gains and increasing tensions in the region".
The cross-Gulf relationship seems to be going down hill rapidly.
Earlier this year Saudi Arabia’s execution of the popular Shia preacher Nimr-al-Nimr wparked protests in several Iranian cities and the burning of the Saudi embassy and a consulate.
That prompted Riyadh to cut off diplomatic ties and the espionage trial opened a month later.
May slams Iran 'threat'
May's remarks at the Gulf Cooperation Council meeting may antagonise Tehran again.
“I want to assure you that I'm clear-eyed about the threat that Iran poses to the Gulf and the wider Middle East,” she said to delegations from Saudi Arabia, Kuwait, Bahrain, Qatar, the United Arab Emirates and Oman.
“The UK is fully committed to our strategic partnership with the Gulf and working with you to counter that threat.”
But May also said that the nuclear deal between Iran and the five permanent members of the UN Security Council and Germany, the P5+1, had made the region safer.
The deal has “neutralised the possibility of Iran acquiring nuclear weapons for over a decade”, she said, adding that Iran has removed 13,000 centrifuges together with associated infrastructure and eliminated 20 percent of its stock of enriched uranium.
“But we must also work together to push back against Iran's aggressive regional actions, whether in Lebanon, Iraq, Yemen, Syria or in the Gulf itself,” she went on.
Her words were not well received in Tehran.
“For Iranians it's extraordinary to see the British prime minister at a conference in a country which is basically quashing any form of dissent on a daily basis,” says Muhammad Marandi, a political scientist with University of Tehran.
“With regard to these countries, the only significant one is Saudi Arabia and Iran's problem with Saudi Arabia has to do with its support for Wahhabi extremism [a reference to the strict school of Islam espoused by the Saudi ruling family and propagated abroad].”
As for the trial of the Shia Muslims, he says, Iranians do not believe it is based on any facts.
“The Saudis are fabricating this story altogether. And this fabrication is a result of the losses that the Saudis are facing in their war against Yemen and their support for what Iranians consider to be extremists in Syria and in Iraq.
“In other words, this is a sort of knee-jerk reaction. Otherwise no one here really believes that the Saudis have discovered a host of people who are spies and that they are going to deal with them in this sudden manner.”
Trump threatens Iran nuclear deal
In the background to all this is the forthcoming US presidency of Donald Trump, who has indicated that he will scrap the Iran nuclear deal.
“The Trump administration will have a very negative effect,” says Rouzbeh Parsi, a lecturer with Lund University. ”The question is how quickly it will have this effect and to what extent.
“We already know that he is against the deal, we already know that his advisors and the people he appointed are very much against the nuclear deal but also against Iran in general.
“So the question now is, how quickly and to what extent is he willing to pursue all these statements and positions, into actual policy."
The Iranians are not rushing to conclusions about Trump for the moment:
“The US presidency for Iran is not something that can be judged yet,” says Marandi. “Iranians feel that Obama was not a good president; he didn't do anything to rebuild Iranian-US ties and even now he is violating the agreement between Iran and the P5+1, by signing in a new law.
“On the other hand, Iranians believe that the US is very much responsible for the rise of extremism in Syria and Iraq and the war in Yemen, as well as the tragedy in Libya.
“But in the case of Trump, the Iranians, despite the rhetoric and the language, during the campaign, Iranians have decided to wait and see and not to pass judgment on him yet,” Marandi says.