Iranian university students attacked the embassy Tuesday, looting buildings, throwing firebombs and briefly seizing six embassy workers.
"Clearly there will be other, further, and serious consequences. I will make a statement updating Parliament" Wednesday, Hague said in remarks reported by The Daily Telegraph.
"There has been a confusing situation at times as to the whereabouts of certain staff. I wouldn't use the term 'hostage.' Clearly there have been situations where the Iranian police have intervened to try to ensure the safety of our staff.
"We are grateful for that but this situation should never have been allowed to arise in the first place," Hague said.
"The safety of our staff is our utmost priority. On our latest information, it now appears that all our staff and their dependants are accounted for. We are urgently establishing the whereabouts of our locally engaged security staff to ensure their well-being."
Sky News reported protesters rushed into the embassy compound, reportedly removing and burning a British flag and replacing it with an Iranian flag.
Students chanted "Down with Britain," "Down with America," "Down with Israel" and "Students are Awake and Hate Britain," Iran's semiofficial Fars News Agency reported.
The students also were shown on Iranian state television throwing stones at embassy windows.
Fars said Iranian police secured the release of six embassy workers who had been seized by students.
Iran's Foreign Ministry issued a statement regretting the attack.
"The Foreign Ministry regrets the protests that led to some unacceptable behaviors. We respect and we are committed to international regulations on the immunity and safety of diplomats and diplomatic places," the statement said.
"News of the utterly deplorable assault today on the British Embassy in Tehran is deeply concerning," Shadow Foreign Secretary Douglas Alexander said earlier, The Daily Telegraph reported.
"The backdrop to these violent events are the recent worrying scenes witnessed in the Iranian Parliament," Alexander said. "Our efforts to prevent Iran acquiring nuclear weapons must continue notwithstanding these appalling scenes."
The protests came after Tehran decided to reduce ties with Britain after London imposed more sanctions on Iran.
Iranian lawmakers Sunday approved downgrading ambassadorial ties with Britain to the charge d'affaires level and were preparing to expel Dominick Chilcott, the British ambassador to Iran, Fars said.
The demonstration occurred as Iran commemorated the first anniversary of the death of nuclear scientist Majid Shahriari in a bombing the Iranian government accused Israel and the West of orchestrating.
The White House issued a statement condemning the attack "in the strongest terms the storming of the British Embassy in Tehran. Iran has a responsibility to protect the diplomatic missions present in its country and the personnel stationed at them. We urge Iran to fully respect its international obligations, to condemn the incident, to prosecute the offenders, and to ensure that no further such incidents take place either at the British Embassy or any other mission in Iran. Our State Department is in close contact with the British government and we stand ready to support our allies at this difficult time."
2014: The Year in Music [PHOTOS]