He 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."
Iranian state TV, quoting a government spokesman, said: "The foreign ministry spokesman...described the move as... hasty and added that naturally the government of the Islamic Republic of Iran would take further appropriate action regarding the issue."
About 24 embassy staff and their dependants were based at the British Embassy and residential compounds in Tehran.
British citizens have been advised against all but essential travel to Iran and those in need of help will be able to get consular assistance from other EU missions in Tehran.
Prime Minister David Cameron called the attack "outrageous and indefensible".
He warned Iran's leaders of "serious consequences" following the breach of international law.
The United States, which cut off diplomatic ties to Iran after students stormed its own embassy in 1979, taking 52 Americans hostage for 444 days, also expressed alarm.
President Barack Obama said the storming of the embassy was "not acceptable" and that "all of us are deeply disturbed".
Tehran police chief General Hossein Sajadinia said several protesters had been arrested and would face the courts.
The break-in came amid protests against what the students described as London's "hostile policies" against Iran.
Iran's parliament voted on Sunday to reduce diplomatic relations with the UK following London's support for increased sanctions on Iran over its nuclear programme.
The West fears Iran is seeking to develop nuclear weapons but Tehran insists the programme is simply to meet its energy needs.
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