Multiculturalism in the UK has left a "terrible" legacy, creating a vacuum that has been filled by extremists from across the political spectrum, the shadow home secretary, Dominic Grieve, warns today.

In an interview with the Guardian on the eve of the Conservative party conference, Grieve says that "long-term inhabitants" have been left fearful, while second- and third- generation immigrants have felt alienated and unsure what British values stand for. He also warns against downplaying Britain's Christian heritage.

His remarks on such a contentious area come as an ICM poll for the Guardian shows that Labour has narrowed the gap on the Tories, whose lead over the government is now into single figures - the lowest since April.

The survey puts the Conservatives on 41%, down three points from last month. Labour is up three on 32% with the Liberal Democrats on 18%.

The poll - the first to be carried out after the end of the Labour conference and the resignation of Ruth Kelly - suggests that voters may be returning to Labour amid fears of a worldwide economic crash, and will underline fears in the Tory party that it has yet to "seal the deal" with the electorate. Based on the poll, the Conservatives would struggle to win an overall majority at an immediate general election.

With polls now suggesting a narrowing of the gap between the two main parties, David Cameron knows he needs to outline how the Tories would address the economic crisis and make a difference in government. The conference has been tightly organised to focus on the economy, the NHS and "fixing broken Britain".

But Grieve today ventures into the sensitive subject of multiculturalism in some of the strongest remarks by a Tory in recent times. He tells the Guardian: "We've actually done something terrible to ourselves in Britain. In the name of trying to prepare people for some new multicultural society we've encouraged people, particularly the sort of long-term inhabitants, to say 'well your cultural background isn't really very important'." He adds: "In this vacuum the BNP rise and Hizb ut-Tahrir rises. They're two very similar phenomena of people who are experiencing a form of cultural despair about themselves, their identity. And it's terribly easy to latch on to confrontational and aggressive variants of their cultural background as being the only way to sort of reassure themselves that they can survive and have an identity."

The shadow home secretary said multiculturalism was inspired by the "understandable" desire to make people feel comfortable. But he added: "The idea behind it was [to] create the melting pot. But the melting pot needs the ingredients of people's confidence in themselves as they come together. And if it isn't there I think we've done ourselves huge damage."

He also raises fears that "fundamental Islam" is restricting debate. "Our country has adapted because people have been tolerant which has often required a lot of forbearance and acceptance of things they didn't like. We all have to accept things we don't like. That is how Britain has evolved. When I go and address an Islamic audience I always point this out."

An Anglican, Grieve praises the contribution all the major religions have made to Britain. But he says that people should not forget Britain's Christian heritage. "The role of Christianity is really rather important. It can't just be magicked out of the script. It colours many of the fundamental viewpoints of British people, including many who've never been in a church."

Grieve says he would restore traditional British justice by conducting a review into whether to scrap fixed penalties for "dishonesty offences", such as shoplifting, though not motoring offences.

• ICM interviewed a random sample of 1,012 adults aged 18+ by telephone between September 24 and 25. Interviews were conducted across the country and the results have been weighted to the profile of all adults.