The fight against terrorism should sit alongside the Civil War, Magna Carta and World War II in a "British story" to foster citizenship, says Jack Straw.
Mr Straw is a contender to be deputy prime minister
The Commons leader said a stronger sense of "Britishness" and its roots in democracy was needed to challenge those opposed to Britain's core values.
Some rights and responsibilities were a non-negotiable part of being a British citizen, he said in a speech.
And it would help reduce segregation in an increasingly mixed society.
Mr Straw, a contender to be Labour deputy leader, sparked a row last year by saying he preferred Muslim women to remove veils when visiting his constituency surgery.
Fight for votes
In a speech on Thursday, part of the Cyril Foster Lecture at Oxford University, he said 8% of the British population were from families who originated abroad, most of whom had integrated well.
But in eight areas - including his own Blackburn constituency - there was increasing segregation.
To foster citizenship a stronger "British story" was needed, he said - as was the case in the US, Canada and Australia.
He said the "fight now against unbridled terror" should be part of the story, alongside the Magna Carta, the fight for votes and emancipation of Catholics, women, ethnic minorities and World War II.
He conceded that the British had often looked or acted like oppressors "to the Irish and to many of the peoples of the British empire".
But he said the freedom preached by Britain helped ensure that the empire had collapsed "with less bloodshed than many other decolonisation struggles".
A stronger "British story" would challenge those with a "single, all-consuming identity" at odds with democratic values, such as minority fringe Muslim groups.
While they represented "an extremely small fraction" of Muslims in Britain, they had been able to "amplify their significance" far beyond what their numbers warranted, he said.
Mr Straw said those who felt detached from British society had to be reassured that they did not have to give up their religion or culture.
And those who felt uneasy about the presence of people from different cultures had to be reassured they were not a threat.
Mr Straw sparked a row about the niqab
"We have to be clearer about what it means to be British," he said.
He said society should stress how democracy could serve "as the means to allow different groups with often competing interests to live together in relative harmony."
But he said, while there was room for "multiple and different identities", they could not take precedence over the British "core democratic values of freedom, fairness, tolerance and plurality".
"To be a British citizen, fully playing your part in British society, you must subscribe to that. It is the bargain and it is non-negotiable."
Mr Straw welcomed an announcement from Education Secretary Alan Johnson that secondary school pupils up to the age of 16 would be taught about shared values and life in the UK in citizenship lessons.