JOIN USA large number of students were staging a noisy protest at both places to denounce what they said was Britain's hostility to Iran.
Some 100 of them forced their way into the British Council building and took six staffers hostage, Xinhua reported. It did give their nationality.
A similar protest saw a similar invasion by students earlier at the British embassy in central Tehran.
At both places, British flags were pulled down and replaced with Iranian flags.
Some of the protesters clashed with riot police and climbed over the gate of the compound.
The riot police failed to prevent them from entering the embassy.
A Xinhua reporter saw the students set fire to the British flag after dragging it down. They demanded the expulsion of the British ambassador.
Some others smashed the windows of the embassy building, took out some documents from the offices of the embassy and set fire to them, the Xinhua reporter said.
The smoke caused by the fire was visible from outside the embassy.
Britain's Foreign Office said it was outraged by the actions and urged Tehran to honour international commitments to protect diplomatic missions and their staff, BBC reported.
The rampage occurred a day after Iran's highest legislative body, Guardian Council of the Constitution, unanimously approved reducing diplomatic ties with Britain in response to its "hostile" policy against Iran.
Britain severed all links with the Iranian banks last week as part of its new sanctions imposed in the wake of a report by the International Atomic Energy Agency (IAEA) that expressed concern over Tehran's controversial nuclear programme.