David Cameron says he is reaching out to voters in the inner cities

The Tory leader said the far-right party held "unacceptable" views and hoped no-one would vote for it.

However, the BNP said there was "no hate at all" in their policies.

Mr Cameron told Sky News' Sunday Live: "The BNP is a party that thrives on hatred, that wants to set one race against another."

The fear is if you are white and you say something that may be considered derogatory by somebody about an ethnic minority, you are going to be sacked or locked up Philip Davies Conservative MP Clarke warns of alienation Profile: BNP

He added: "I hope nobody votes for the BNP. I would rather people voted for any other party."

A Sunday Mirror poll suggested 45.5% of those certain to vote in the London borough of Barking and Dagenham said they would vote BNP, and 7% of those planning to vote in Bradford would do so.

The newspaper questioned 496 adults face-to-face in Barking and Dagenham and Bradford on April 20 and 21.

If the Barking result translated into real votes, the newspaper said, the BNP could become the official opposition in the borough.

Phil Edwards, national press officer for the British National Party, said: "There is no hate at all in our policies, just fact.

"This proves, really, that the BNP is the only opposition party in this country."

Second largest

On Sunday Philip Davies, the Conservative MP for Shipley in West Yorkshire, blamed mainstream parties for the apparent rising popularity of the BNP, accusing them of failing to reflect people's concerns over immigration and race relations.

He told the Observer newspaper people were so afraid of expressing their opinions, the only way to do it was to "put a cross in a secret ballot for the BNP".

"The fear is if you are white and you say something that may be considered derogatory by somebody about an ethnic minority, you are going to be sacked or locked up", he said,.

But shadow home secretary David Davis moved to dampen suggestions that Mr Davies' comments were an implicit criticism of his leader's overall strategy to move to the political centre ground.

Control immigration

Mr Davis told ITV's Jonathan Dimbleby programme: "What he said in the middle of it was that David Cameron and he agreed on immigration...about the need to control immigration in order to get good race relations within the country."

Barking's Labour MP Margaret Hodge has also warned that eight out of 10 white voters she spoke to were considering a switch to the BNP.

Home secretary Charles Clarke has also said people's concerns on crime and immigration must be tackled, although he said Ms Hodge had overstated the threat from the BNP.

And Liberal Democrat President Simon Hughes has urged voters not to be taken in by the "simplistic promises" of the BNP, but said that the main parties had only themselves to blame if people were turning away from them.