Only two out of 10 people believe that Ed Miliband has what it takes to be a good Prime Minister, according to an opinion poll for The Independent which highlights the mountain the Labour leader still has to climb.

ComRes found that almost twice as many people think David Cameron can be a good Prime Minister, and the Conservatives are more trusted on the economy than Labour despite the slide back into recession.

In a highly personal speech to the Labour conference today, Mr Miliband will contrast his education at a London comprehensive school with the privileged background of Mr Cameron, who went to Eton. "My family hasn't sat under the same oak tree for the last 500 years," he will say. But Labour officials denied that Mr Miliband is reigniting the class war.

He will tell the Manchester conference how his parents came to Britain as Jewish refugees from the Nazis. "I would not be standing here today without the compassion and tolerance of our great country, Great Britain, a country that my parents saw rebuilt after the Second World War," he will say.

"I was born at my local NHS hospital, the same hospital where my two sons were born. And I went to my local school with people from all backgrounds. I still remember the motivation, the inspiration from some amazing teaching."

According to ComRes, only 22 per cent of people believe Mr Miliband has what it takes to be a good Prime Minister, while 63 per cent do not. Labour supporters are split down the middle about his ability to lead the nation. Some 44 per cent think that he has what it takes, but 42 per cent do not.

Although a majority of people (52 per cent) do not believe Mr Cameron has what it takes to be a good premier, 39 per cent do – a much higher rating than Mr Miliband's. Four in five Conservative voters (81 per cent) agree that Mr Cameron "has what it takes", compared with 41 per cent of Liberal Democrat supporters and 21 per cent of Labour voters.

The findings show why Labour decided to use its conference to tackle Mr Miliband's credibility gap as a potential Prime Minister. Last night his aides insisted he is unknown rather than disliked, and pointed to recent surveys showing his net approval rating is now higher than Mr Cameron's. They said prime ministers often outscored opposition leaders because they were already doing the job.

But Labour appears to have made little progress on gaining trust for economic competence this year. Only 24 per cent of people say they trust Mr Miliband and the shadow Chancellor, Ed Balls, to make the right decisions on the economy, while 64 per cent do not. The figures are little changed since January, when they stood at 24 per cent and 65 per cent respectively.

Only half of Labour voters (50 per cent) now trust the party's top two figures to make the right economic decisions, while 40 per cent do not. Nor do four in five Conservative supporters (80 per cent) and 69 per cent of Liberal Democrat voters.

Some 30 per cent of people trust Mr Cameron and the Chancellor, George Osborne, to make the right calls on the economy, while 62 per cent do not. One in five Conservative voters (22 per cent) do not trust the Cameron-Osborne team to get them right.

Labour's seven-point lead in the last ComRes survey for The Independent a month ago has dropped to just three points. The Liberal Democrats appear to have secured a bounce from the publicity their autumn conference attracted last week. Labour is now on 38 per cent (down four points on last month), the Conservatives on 35 per cent (no change), the Liberal Democrats on 15 per cent (up three points) and other parties on 12 per cent. These figures would give Labour a majority of 24 at a general election fought on the existing boundaries.