Baroness Warsi, the shadow community cohesion minister, said Labour's "state-driven multiculturalism" had cemented division in society.
A Tory government would ensure all immigrants learnt English and schoolchildren were properly taught British history, she said.
The Baroness told the Conservative Party conference in Birmingham her parents, who came to the UK from the Punjab, "instinctively knew about integration".
She said: "They knew what Britain stood for and they wanted to be a part of it.
"And it was a Conservative government that provided them with their opportunities to get on.
"Contrast that with Labour over the last 10 years - presiding over a decade of state-driven multiculturalism which has played on our differences and, let's be honest, too often for what Labour saw as selfish political advantage.
"It has sent out the message that we're not sharing a society; we're just co-habiting a space.
"It's led people to retreat into separate cultures rather than reach for a shared community.
"Its policy of hand-outs as opposed to hand-ups has led to appallingly low levels of social mobility
"And their obsession with self-appointed community leaders and crude use of patronage politics has led to communities divided against each other."
The Baroness said the approach had led to some people losing the "inner instinct" of what it is to be British.
She said: "What deeply concerns me is the Government's attempt to unify us through a sense of state Britishness.
"An identify forged out of gimmicks, slogans and flag planting on lawns as opposed to an identity forged on real opportunities for all, steeped in our history and built on a shared national language."
Setting out her plans for a new sense of community spirit, she told party supporters: "In some places, we've completely lost the feeling of neighbourliness.
"The ease of sharing the little things - the school run, the cup of sugar, the chat over the garden fence.
"Now our communities are going to keep coming up against one another. Different cultures are going to carry on having conflicts.
"And to fix our society, to revive that spirit of community, we're going to need to recapture that feeling of neighbourliness."
The Tories were putting "integration and neighbourliness" at the heart of their policies, she said.
"Good neighbours talk to each other. That's why we will ensure that English is spoken by all who choose to make Britain their home.
"Good neighbours understand each other, where they're from and where they're going. That's why we will ensure that we properly teach British history so that our young people know who we are as a nation.
"Good neighbours don't resent each other. That's why we will support community groups based on their effectiveness, and not on the basis of their race or religion.
"Good neighbours look out for each other. That's why we will tackle unacceptable cultural practices, we won't turn our backs and say it's too sensitive and may offend, that it's none of our business. We will deal with these issues head on."
:: During the four-day conference Conservatives, including many of David Cameron's frontbench team, will be taking part in a social action project on Birmingham's deprived Welsh House Farm estate.
Delegates from the conference will be helping to refurbish the youth centre and improve the outdoor sports area by planting bulbs, clearing shrubs, painting and cleaning.
Baroness Warsi said: "Social action is simply about being good neighbours."
Dods Parliamentary Communications Ltd