The head of the Kerman region's revolutionary court, Dadkhoda Salari, told the agency the suspect made contact with British agents 11 times in recent months, inside and outside the country.
According to Salari, the suspect has admitted his guilt and has been put on trial.
It has not been suggested the alleged spy is a Briton, and Tehran has a history of announcing the arrest of people it claims are spying without releasing further details.
According to a report from Iran's conservative news agency Tasnim, the alleged spy was arrested after 10 months of intelligence work and had once had a meeting with British agents in London.
It quotes Salari as saying he is aged over 50, with an "academic education". He is said to be fluent in English but does not hold an official post.
A spokeswoman for the Foreign Office in London said: "We don't comment on intelligence matters."
Iran's envoy to the UK last week made his first visit to London, during which he met officials at the Foreign Office.
London, meanwhile, announced the appointment of Ajay Sharma as non-resident charge d'affaires in Iran in November, and Sharma made his first visit to Iran in that role this month - the first by a British diplomat for two years.
Sharma said he had "detailed and constructive discussions" about the UK's relationship with Iran.
He also visited the site of the British embassy in Tehran to assess the damage following the mob attack two years ago.
Foreign Secretary William Hague has said relations between the two countries were improving on a "reciprocal basis".
Thawing relations between Tehran and the international community have also seen a temporary deal reached over its nuclear programme.
Iran last month agreed to curb some of its nuclear activities in return for £4.3 billion in sanctions relief, after days of talks in Geneva.
The country agreed to give better access to inspectors and halt some of its work on uranium enrichment for a six-month period.
However, the agreement appeared to face its first major difficulty on Friday, with Russia warning that expanding a US sanctions blacklist could seriously complicate the deal's implementation.