Alireza Akbari, 61, who was allegedly tortured to force a confession, was executed on Saturday after being accused of being a MI6 spy.
Mr Akbari had denied all the charges against him after his arrest in 2019.
UK Prime Minister Rishi Sunak said the execution was a "callous and cowardly act, carried out by a barbaric regime".
The Daily Telegraph now reports that the UK is now reconsidering its support for the Obama-era nuclear agreement, which had eased sanctions on Tehran in exchanging for it halting its nuclear programme.
Senior Whitehall sources told the paper the "landscape" had changed significantly since the negotiation process began and Britain was reviewing its options.
"During the time we have been dealing with it, the landscape and proposition has completely changed - largely because of the behaviour of the Iranian regime," a government source said.
It came after the British government announced it was sanctioning Iran’s prosecutor-general after Mr Akbari was hanged.
Foreign secretary James Cleverly, who has also summoned Iran’s charge d’affaires, said the sanctions underlined the UK’s disgust at the execution, adding that prosecutor general Mohammad Jafar Montazeri was "at the heart of Iran’s use of the death penalty".
Alicia Kearns, chair of parliament’s foreign affairs select committee, called for the UK to change its stance and come down tougher on Iran, "especially to make us safer in the UK by shutting down incubators of Iranian hostilities in London and beyond".
Ms Kearns labelled the country "a terrorist state", responsible for the most attempted murders in the UK and the most assassinations in western Europe.