At least 180,000 Kurds were killed by Saddam Hussein’s forces.
The justice4genocide campaign says many more died in atrocities carried out by regimes from the 1960s onwards.
It is petitioning the UK government to declare the mass killing of Kurds as a genocide and press the European Union and United Nations to do the same.
The campaign has the support of a number of British MPs and the Kurdistan Regional Government (KRG).
The KRG’s representative in Britain, Bayan Sami Abdul Rahman, said she hoped the campaign would eventually lead to trials at the international criminal court.
Ms Rahman said: “Different people were responsible through different decades, so there are many, many people who have blood on their hands.
“Even though Saddam Hussein was charged with genocide he wasn’t actually tried for genocide so that’s another frustration for survivors.”
Both Hussein and his cousin, Ali Hassan al-Majid – known as Chemical Ali – were put to death.
Towards the end of the Iran-Iraq war, they targeted the Kurdish population in the north of Iraq.
In the most notorious attack, warplanes dropped chemical bombs on the town of Halabja, killing 5,000 men, women and children.
Shaho Qadir was 13 at the time. A bomb blew off both his legs. “It was like a nightmare for me. It was just unbelievable – in one second losing your legs. You can’t believe it,” he said.
Mr Qadir joined justice4genocide to gather signatures for their petition in London, where campaigners read out the names of some of those killed.
A spokesperson for the British Foreign Office said: “It is clear that appalling atrocities have been perpetrated against the Iraqi Kurds and other minorities.
“We have always condemned those crimes, which caused so much suffering to so many people.
“Today, we work closely with all of the people of Iraq to help support a stable, democratic and prosperous country where such atrocities can never happen again.”
BBC World Service News reporter, 27 October 2012