I have good news for David Cameron – and also a warning and some urgent advice.

The good news is that the Conservatives have opened up a clear lead when people are asked YouGov’s “forced choice” question – would people rather be governed by a Conservative government led by David Cameron or a Labour government led by Ed Miliband. In our new year poll for Prospect, the Tories lead by 41% to 36%. This five point lead is the highest for two years.

It compares with a Labour lead of three points when the same people are asked our conventional voting intention question. The contrast between the two figures is explained largely by the views of Ukip supporters, who divide 50-18% in favour of the Tories. Doubtless, the Tories feel frustrated that so many of their past supporters have moved to Ukip. However, our figures suggest that the Tories may be able to win many of them back in the key marginals by stressing their message, “vote Farage, get Miliband”.

Now for the warning. The Conservative lead in our forced choice question may have grown, but the level of support for the Tories has not grown. Apart from a brief dip, following 2012’s “omnishambles” budget, it has been a constant 40% +/-1 for the past two years. Rather, support for Labour has declined, while the ranks of the don’t knows have swollen.

This is consistent with other YouGov evidence. Our conventional voting figures have seen Labour support drop from the low 40s a year or so ago to the low 30s today. Miliband’s reputation and Labour’s support have declined, but Cameron’s and the Conservatives’ figures have not improved. In short, many voters have lost faith in Labour but not transferred their affections to the Tories.

That helps to explain why Ukip, the Greens and the SNP all stand higher than a year ago, but the Conservatives do not. That in turn explains why the Tories might harbour hopes of once again being the largest party on election day, but remain well short of the support they need to win outright. Frightening Ukip supporters with the nightmare of a Miliband government could help the Tories remain ahead of Labour – but won’t be enough to reach the 326 seats needed for an overall majority in the new House of Commons.

Cameron’s challenge, then is not just to attack Labour but to improve his own reputation and that of his party. This is where we turn to the urgent advice. It is rooted in YouGov’s special analysis for Prospect on the elements of the Cameron and Tory “brand” that need to be burnished.

We tested eight statements about the Prime Minister and his party: three positive and five negative. Four of the statements, all negative, attracted overwhelming support, with at least 63% in agreement and no more than 24% disagreement. Run them together and they sound like a bitter repudiation of the party that has dominated British politics for much of the past two centuries: “David Cameron doesn’t understand the lives of people like me. The Conservatives care more about the rich and affluent than ordinary people. The Conservatives are too close to big business and the banks. Underneath the surface the Conservative Party contains many people with bigoted and intolerant views.”

That is a terrible indictment, made worse by that fact that each statement secures the agreement of one in four loyal Tories – those who voted for the party in 2010 and would do so today.

At the other end of the scale, just 25% agree with one of the positive statements, while 60% disagree: “The Conservative party cares about helping all groups in society, not just the few.” In between are three statements that attract more mixed responses, with the proportions agreeing and disagreeing hovering between one-third and a half. Thus a plurality of 48-39% agree that “The Conservatives are prepared to take the tough but necessary decisions the country needs”. Against that, more people disagree (48%) than agree (34%) that “the Conservative party have changed for the better since their time in opposition”, while the public is evenly divided on the proposition that “David Cameron has no clear principles” (34% agree, 48% disagree).

On the age-old principle that the twin objectives of improving a party’s “brand” are to build on the positives and neutralise the negatives, the first half of the task is clear. The economy and deficit reduction provide Cameron with his best “re-elect me” message. Until recently, the Tories’ lead over Labour on managing Britain’s finances was offset to some extent by the figures, frequently and understandably exploited by Miliband, that even though gross domestic growth had started to grow again, living standards were stalled. This spring, the Tories may be able to fend off this argument. The glut of oil in world markets has reduced the cost of petrol, and fierce competition among supermarkets has cut the price of many basic groceries.

So: Cameron has good reason to hope that he can sustain his personal lead over Miliband and win the argument on the economy. But, in my judgement, to win a clear overall majority he must also address his and his party’s dire negative ratings.

What does this mean? A good place to start is the three-million-plus voters who have deserted the Tories since the last election. Many have switched to Ukip, but there are also a fair number of don’t knows. (A few have defected to Labour, hardly any to the Liberal Democrats or Greens.) If the Tories are to win outright this May, they will have to woo back many of these deserters.

The anti-Tory message that chimes most with them is personal: “David Cameron doesn’t understand the lives of people like me”. Fully 74% of defectors agree with this, against 61-64% for the other widely-endorsed negatives.

There are two possible responses to this finding. One is that Cameron is toxic among a crucial group of voters and should be hidden as far as possible from public view. The other is that he must do more to regain the approval of many voters who supported him five years ago. Even if the first option makes theoretical sense (which I don’t think it does), it is wholly impractical. In modern elections party leaders are inevitably the focus of media attention. The Tories have no choice but to cast Cameron in the best possible light.

His problem, of course, is that as an old Etonian Oxford graduate from a prosperous family, he cannot escape being seen as a toff. But past, even posher Tory leaders have managed to persuade voters that they seek to advance the cause of the whole country, not just the rich and well-connected.

Cameron’s decision to send his children to state schools helps. But the best thing he can do is to develop policies that show he really is prepared to stamp on bad behaviour by banks and business – from tax avoidance and undeserved bonuses to backing the living wage campaign and then enforcing it rigorously. He could also retreat from his ill-judged “bedroom tax” on poor families. He may not be able to get voters to believe that “we are all in it together”, but he can at least seek to show that he and his ministers are actively committed to siding with the people against the plutocrats. A few angry looks from his well-heeled Oxfordshire constituents may be the price he must pay for securing a nation-wide majority in May.

This analysis appears in the February issue of Prospect

See the full Prospect results here