David Cameron has failed to seal the deal with the British public, who believe the Conservatives would govern for the well-off and are not an attractive alternative to Labour.

In a remarkable snapshot of national opinion just months ahead of the general election, a ComRes poll for The Independent found that people disagree with the statement that "the Conservative Party offers an appealing alternative to the Labour Party", by a margin of 49 to 45 per cent.

Meanwhile, by 52 to 44 per cent, the public agrees with the statement that "a Conservative Government would mainly represent the interests of the well-off rather than ordinary people".

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The survey gives the Tories a nine-point lead over Labour, down one point on last month. If repeated at a general election, the figures would leave the Tories five seats short of an overall majority in a hung parliament. According to ComRes, the Tories are on 38 per cent (up one point on last month), Labour 29 per cent (up two points), the Liberal Democrats 19 per cent (down one point) and others 14 per cent (down two points).

The findings will add to the jitters in the Tory high command after the gap between the two main parties closed in recent weeks. Amid fears that the Tory message has been too "austere" because of the economic crisis, Mr Cameron will try to paint a more positive vision of life under a Tory government in a new year campaign.

The survey will encourage those Labour strategists who are anxious to win back the party's traditional supporters. Mr Brown was accused of reigniting the class war after he said that the Tory policy of cutting inheritance tax was "dreamed up on the playing fields of Eton", where Mr Cameron was educated.

Although ComRes found that the Tories enjoy a 20-point lead among the AB top social group, the two main parties are virtually neck and neck among the other groups. Twice as many C2 skilled manual workers and the bottom DE group are "certain not to vote" than are ABs.

Labour appears to have clawed back some of its traditional support since this month's pre-Budget report. The proportion of those who backed Labour in 2005 and who would stick with the party has risen from 66 to 76 per cent.

The Tories appear still to have work to do among women voters. They are 11 points ahead of Labour among men but only six points ahead among women.

There is some good news for the Conservatives in today's poll. By a margin of 55 to 38 per cent, people support the party's policy of raising the threshold for inheritance tax to £1m. This will encourage Mr Cameron to resist pressure to ditch the idea. The finding suggests that aspirational voters like the policy and do not necessarily buy Labour's line that it would only help millionaires.

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Sixty-three per cent of the top AB social group agree with the Tory policy, falling to 48 per cent among the bottom DE group. As expected, Conservative voters are the most enthusiastic about this policy – 64 per cent agree. Surprisingly, more Labour voters agree than disagree with it – by a margin of 50 to 42 per cent.

Worryingly for Labour, the public is evenly divided over whether a Labour government would protect front-line public services such as health and education better than a Tory government would – seen by Mr Brown as the key dividing line between the two main parties. Some 47 per cent agree with this statement, while 46 per cent disagree.

People in lower income brackets are more likely than those in higher income brackets (by 54 to 47 per cent) to agree that a Conservative government would mainly represent the interests of well-off people. Thirty per cent of Tory voters agree, as do 78 per cent of Labour and 64 per cent of Lib Dem voters. Worryingly for the Tories, 45 per cent of the "don't knows" (or those who refuse to say how they would vote) also agree with this statement.

Senior Tories will be most concerned about the lukewarm support for the party. Although the public has lost faith with Labour, it has not sufficiently warmed to the Conservatives for their liking. Women are less likely than men to regard the Tories as an attractive alternative to Labour.

With the exception of people aged 65 and over and the 18-24 age group, the majority of people in all the other age brackets do not regard the Tories as an attractive alternative.

ComRes phoned 1,006 British adults between 19 and 20 December 2009. Data were weighted by past vote recall. ComRes is a member of the British Polling Council and abides by its rules. Full tables at www.comres.co.uk.