David Cameron is facing renewed demands to embrace a sugar tax to tackle Britain’s growing obesity crisis after a new poll found more than half of voters backed the idea.

Support for a levy on sugary drinks and food is now running at 53%, according to the findings, shared with the Observer, of a representative sample* of more than 2,000 people. ComRes asked them: “To what extent do you support or oppose the introduction of taxes on unhealthy food and drinks to improve child health?”

The poll comes at the end of a week in which the government’s health advisers recommended urgent adoption of a sugar tax, but the prime minister made clear his strong opposition to it. The disclosure that a majority favour such a move, even though it would increase the cost of many soft drinks and sweet foods, has prompted senior doctors to urge Cameron to include it in his forthcoming strategy to tackle childhood obesity.

“The groundswell of support for taxes on unhealthy food and drinks in order to improve the health of the nation is becoming increasingly difficult for government to ignore,” said Professor Neena Modi, president of the Royal College of Paediatrics and Child Health, which commissioned the poll.

A coalition of health professionals, academics, scientists, nutritionists and children’s health campaigners now wanted a sugar tax because the evidence from countries such as Mexico was that it helped reduce consumption, Modi said, adding that it was time to bin the government’s failed Responsibility Deal, which since 2010 has relied on voluntary action by food and drink firms. “We ask the prime minister to accept the clear evidence that the last five years of trying to encourage industry to voluntarily make their products healthier simply has not worked. It is unacceptable to put the health of our children, and the generations to come, at risk by placing responsibility in the hands of those with vested interests.”

NHS England chief executive Simon Stevens said: “There’s growing support for broad-based action to encourage – and where necessary force – manufacturers to decisively cut the added sugar they ladle into children’s fizzy drinks and junk food.”

But a Downing Street spokesman insisted: “The prime minister has been clear that there are more effective ways of tackling this issue than a sugar tax, which is why we are developing a comprehensive strategy looking at all the factors that contribute to a child becoming overweight.”

Public Health England highlighted sugar’s key role in soaring obesity in its report last week, which health secretary Jeremy Hunt initially tried to keep secret. It urged “a price increase of a minimum of 10%-20% on high-sugar products through the use of a tax or levy”.

Jamie Oliver is introducing a sugar levy in his restaurants. Photograph: Tristan Fewings/Getty Images

Television chef Jamie Oliver, who plans to introduce a sugar tax on fizzy drinks in his restaurants, criticised Hunt for burying PHE’s government-commissioned report. “Would he rather be remembered, like many of his predecessors, as a politician who dithered when faced with a major crisis or as someone who took logical and radical action and made a positive difference? On this evidence, I fear the former.”

Doctors are also demanding that ministers compel food producers to strip out sugar in yoghurt, sauces and cereals, not just cakes and sweets.

The Academy of Medical Royal Colleges, which represents all 240,000 British doctors professionally, said it backed fiscal measures to reduce sugar intake, but that a sugar tax “is probably not top of the list” of steps that need to be taken to achieve that goal. “Higher up would be reformulation of food, which was very successful in cutting salt consumption, and we should curtail marketing of overly sweetened drinks and food like breakfast cereals to children,” said Professor Dame Sue Bailey, its president.

Graham MacGregor, a professor of cardiovascular medicine and chairman of Action on Sugar, said: “The most important way of reducing calorie intake from sugar reduction would be reformulation, which has been successfully carried out in the UK with salt, so that most of the products we now purchase from supermarkets have been reduced in their salt content by 30-40% without the consumer necessarily being aware of it.”

The 15% average fall in salt intake per head since the early 2000s had prevented about 9,000 deaths from strokes and heart attacks every year, he said. “Exactly the same reformulation could be done for sugar, particularly in soft drinks, as removing the sugar does not reduce the volume of the drink. A 40% reduction in sugar added to drinks and food, done slowly over the next five years, would reduce calorie intake by 100 kcal a day per person in the UK.”

However, the government would need to re-establish an effective, independent agency to push through reformulation, modelled on the Food Standards Agency as it operated under the Blair government, which oversaw gradual salt reduction, MacGregor added.

He also called, in a blog for the New Scientist, for “a ban on marketing of all unhealthy foods, just like cigarettes. There is no rationale for banning cigarette advertisements when unhealthy food is now a much bigger cause of death in the UK. We need also to stop price promotions in supermarkets, which are almost entirely on the most unhealthy foods and encourage greater consumption. We also need to limit availability and portion size. If all of these actions were put into place, we could prevent the development of obesity and type 2 diabetes.”

*ComRes interviewed 2,191 British adults online from 14-18 October 2015. Data was weighted by age, gender, region and socio-economic group to be representative of all British adults aged over 18