"Alireza Akbari, who was sentenced to death on charges of corruption on earth and extensive action against the country’s internal and external security through espionage for the British government's intelligence service ... was executed," Mizan said.
The report accused Akbari, arrested in 2019, of receiving payments of 1,805,000 euros, 265,000 pounds, and $50,000 for spying.
In an audio recording purportedly from Akbari and broadcast by BBC Persian on Wednesday, he said he had confessed to crimes he had not committed after extensive torture.
Sunak said on Twitter he was "appalled by the execution". Cleverly said in a statement it would "not stand unchallenged". "We will be summoning the Iranian Charge d’Affaires to make clear our disgust at Iran’s actions."
British statements on the case have not addressed the Iranian charge that Akbari spied for Britain.
Iranian state media broadcast a video on Thursday that they said showed that Akbari played a role in the 2020 assassination of Iran's top nuclear scientist, Mohsen Fakhrizadeh, killed in a 2020 attack outside Tehran which authorities blamed at the time on Israel.
In the video, Akbari did not confess to involvement in the assassination but said a British agent had asked for information about Fakhrizadeh.
Iran’s state media often airs purported confessions by suspects in politically charged cases.
Reuters could not establish the authenticity of the state media video and audio, or when or where they were recorded.
Akbari was a close ally of Ali Shamkhani, now the secretary of Iran’s Supreme National Security Council, who was defence minister from 1997 to 2005, when Akbari was his deputy.
'3,500 HOURS OF TORTURE'
Reflecting Iran's worsening ties with the West, London-Tehran relations have deteriorated in recent months as efforts have stalled to revive Iran's 2015 nuclear pact, to which Britain is a party.
Britain has also been critical of the Islamic Republic's crackdown on anti-government protests, sparked by the death in custody of a young Iranian-Kurdish woman in September.
A British foreign office minister said on Thursday that Britain was actively considering proscribing Iran's Revolutionary Guard as a terrorist organisation but has not reached a final decision.
Iran has issued dozens of death sentences as part of the crackdown on the unrest, executing at least four people.
In the audio recording broadcast by BBC Persian, Akbari said he had made false confessions as a result of torture.
"With more than 3,500 hours of torture, psychedelic drugs, and physiological and psychological pressure methods, they took away my will. They drove me to the brink of madness... and forced me to make false confessions by force of arms and death threats," he said.