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Five Iranian gunmen were killed and one was arrested. Nineteen hostages were set free but one died and two were injured in the cross-fire.
Millions of people watched the rescue live on television as bank holiday entertainment on all three channels was interrupted to show the real-life drama unfold.
More than 30 masked troops stormed the embassy building from the balcony and front and back doors throwing grenades through the windows.
Screams were heard from inside the building and some 15 minutes later the hostages emerged and were escorted by Scotland Yard police to waiting ambulances.
The siege began five days ago when six gunmen took over the Iranian embassy in Kensington.
Most of their hostages were fellow Iranians but also included embassy police guard PC Trevor Lock, BBC sound man Sim Harris, BBC news organiser Chris Cramer and tourists who had stopped by to collect visas.
Four of the captives - including Mr Cramer - were released over the last week for medical reasons.
The gunmen belonged to a dissident Iranian group opposed to Ayatollah Khomeini, the religious leader who came to power last year.
They wanted the release of 91 political prisoners held in Iran as well as an aircraft to take them and the hostages out of the UK.
The Home Secretary William Whitelaw ordered the attack on the sixth day of the siege after the gunmen shot dead Iranian press attaché Abbas Lavasani and dumped his body outside the building.
Speaking through PC Lock who relayed the demands from an embassy window to police officers on the ground, they then threatened to kill the rest of the hostages and blow up the embassy if their demands were not met.
The Iranian government approved the use of force and President Bani-Sadr announced the SAS raid as a victory. In a broadcast he said "We did not surrender, we became victorious."
The Prime Minister Margaret Thatcher has visited the SAS barracks in Kensington to congratulate the troops on a successful mission, codenamed Operation Nimrod.
It later emerged that during the SAS raid PC Trevor Lock had tackled the leader of the gunmen known as Salim and saved the life of an SAS soldier. He was awarded the George Medal for his actions.
The excellent publicity provided by unprecedented live TV coverage of the event ensured the future of the SAS regiment was guaranteed. It had previously been under threat of disbandment.
The one surviving gunman, Fowzi Nejad, was sentenced to life imprisonment nine months later.
His fellow hostage-takers had opposed Ayatollah Khomeini and demanded freedom for the southern Iranian province of Khuzestan. But their cause was soon forgotten when war broke out between Iran and Iraq in late 1980 - a conflict that was to last eight years.
Although Iran had supported the SAS raid, it took about 13 years for a mutual compensation package to be agreed whereby the British government paid for the damage done to the Iranian embassy and Iran repaired the British embassy in Tehran damaged during the 1979 revolution.
Chris Cramer went on to become managing editor of CNN International.
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