Iran has denied visas for any British staff and all local employees resigned after being summoned to the president's office, the council says.
The council, which promotes cultural and educational ties, says pressure has been growing over its activities.
An Iranian embassy spokesman in London said he would investigate the report.
'Deliberate act'
There have been no British staff at the council since Tehran stopped granting visas two years ago, the council's London-based chief executive, Martin Davidson, told the BBC News website.
Martin Davidson said he was ''very angry'' about the move by Iran
That left its 16 local employees, most of whom were summoned to the Iranian Office of the President in December, where they were ordered to resign from their posts, Mr Davidson said.
"It was a very deliberate act that essentially made it impossible for us to operate there," he added.
Earlier in December, two Iranian staff members had their passports confiscated while trying to leave the country to attend a meeting.
"These actions by the Iranian authorities are unacceptable," Mr Davidson said. "They are designed to pressurise our staff with the clear intention of stopping our cultural and educational work in the country."
The organisation said operations would resume only when employees are able to conduct their work "without fear of intimidation or harassment".
'No winners'
The British Council says about 13,000 Iranians took part in its programmes in Tehran last year, which included English lessons and university and research partnerships.
The council's Iranian partners have also been instructed to reduce or stop their work with the organisation, Mr Davison said.
"There are no winners here," he said. "Our staff in Iran have lost their jobs, our Iranian partners have lost opportunities to work with the UK, and young people in Iran and the UK have lost the chance to build links that can last a lifetime."
Mr Davidson says there are a range of Iranian cultural centres in the UK, which serve a similar purpose to the British Council in Tehran.
"The end result is that they are keen to have a relationship, but they are not prepared to have a two-way street," he says.
Mr Davidson says he hopes to meet the Iranian authorities to work out an agreement to resume work.
There has been no comment yet from Iranian officials.
