Prime Minister David Cameron warned Iran of "serious consequences" as Britain also withdrew its diplomatic staff and families from Tehran.
Making a statement in the House of Commons, Foreign secretary William Hague said Britain had now closed its embassy in Tehran and had evacuated all its 'UK-based' staff.
He said: "The Iranian Charge in London is being informed now that we require the immediate closure of the Iranian Embassy in London and that all Iranian diplomatic staff must leave the UK within the next 48 hours".
Hague added: "If any country makes it impossible for us to operate on their soil they cannot expect to have a functioning Embassy here. This does not amount to the severing of diplomatic relations in their entirety.
It is action that reduces our relations with Iran to the lowest level consistent with the maintenance of diplomatic relations".
Cameron said: "The attack on the British Embassy in Tehran was outrageous and indefensible. The failure of the Iranian government to defend British staff and property was a disgrace".
He added: "We hold the Iranian Government responsible for its unacceptable failure to protect diplomats in line with international law. The Iranian Government must recognise that there will be serious consequences for failing to protect our staff".
The attack on the British embassy followed Britain's decision to impose further sanctions on Iran over its nuclear programme. Norway said it had closed its embassy, citing security concerns.
Hague said: "Yesterday I called the Iranian Foreign Minister to protest in the strongest terms about these events and to demand immediate steps to ensure the safety of our staff and of both Embassy compounds He said that he was sorry for what had happened and that action would be taken in response".
Iran said it regretted the incident, which it described as "unacceptable behaviour by a small number of protesters".
Last week, Britain said it would sever all financial ties with Iran, after a new report by the UN's nuclear watchdog (IAEA) said Iran had carried out tests "relevant to the development of a nuclear device".
Iran denies the accusations, saying its nuclear progamme is solely for civilian purposes