David Cameron is struggling to ease voters' concerns that there is a hidden side to him and his party, a poll for The Independent on Sunday reveals today.

With an election looming, 56 per cent of people believe the Tory leader is a "slick salesman, but I worry about what he is like underneath", the ComRes survey found. Thirty-six per cent disagree with this.

Mr Cameron, in a webcameron broadcast yesterday, took the step of appealing to Labour voters to have an "open mind" at the election, even if they have never voted Tory before.

His plea underscored fears in the Conservative leadership that doubts remain among the public about the party's plans for government, despite expectations that the Tories will win the election.

Today's poll puts the Conservatives on 40 per cent, 11 points clear of Labour. The last ComRes survey for The Independent showed a seven-point gap. The Liberal Democrats are up two points, on 21 per cent.

Outside the South-east, those who are concerned about another side to Mr Cameron outnumber those who are not concerned by a factor of two to one. The poll also reveals that 50 per cent of people believe Gordon Brown has a "warm, human side".

Seven out of 10 voters believe the outcome of the election, expected on 6 May, will be close.

In an attempt to broaden his party's appeal after a negative reaction to Tory plans for spending cuts, Mr Cameron said: "The hopes you had with Labour – that Britain would become a stronger, fairer society – those hopes don't just die because Labour haven't achieved them. They're alive with us in the modern Conservative Party.

"So, please, have an open mind at the next election. Even if you've never voted Conservative before, think about voting for us this time... We're winning the argument on the economy and on building a fairer society. So come and join us."

The plea mirrors that made by Tony Blair to Tory voters in 1997.

In his weekly podcast yesterday, the Prime Minister stepped up pressure on banks to curb bonuses, due this week, after reports that awards have increased by 40 per cent.

Mr Brown also made clear that the UK is close to agreement on a new tax in the form of a global bank levy – either a financial transaction tax or an annual insurance fee, favoured by the United States.

Mr Brown said: "I'm sure you share my anger with some of the banks... it is only fair that those who contributed to the recession and have now benefited from taxpayers' support give something to society in return."

In a separate development, Labour failed to rule out plans for a 10 per cent tax on estates to pay for free social care for the elderly.

Claims yesterday that the polling company Ipsos Mori was canvasing voters with the plan were seized on by the Conservatives. The Tories warned last week that Labour was planning a £20,000 "death tax" to pay for free social care.