The government will consider introducing a "fat tax" to tackle Britain's growing obesity levels, the prime minister, David Cameron, has said.

Cameron said drastic action was needed to prevent health costs soaring and life expectancy falling.

Under measures introduced in Denmark recently, a surcharge is being placed on foods that contain more than 2.3% saturated fat. The levy targets high-fat products such as butter, milk, cheese, pizza, meat, oil and processed food.

Danish consumers have criticised the move, which has left many retailers complaining of excessive bureaucracy.

However, Cameron said the introduction of a similar idea in the UK should not be ruled out.

"I think it is something that we should look at," he told 5 News during a round of broadcast interviews at the Tory conference in Manchester. "The problem in the past when people have looked at using the tax system in this way is the impact it can have on people on low incomes.

"But frankly, do we have a problem with the growing level of obesity? Yes. Do we have a kind of warning in terms of – look at America, how bad things have got there – what happens if we don't do anything? Yes, that should be a wake-up call."

He added: "I am worried about the costs to the health service, [and] the fact that some people are going to have shorter lives than their parents."

He warned that obesity was on the verge of overtaking smoking and drinking as the biggest health challenge facing Britain.

"Don't rule anything out, but let's look at the evidence and let's look at the impact on families," he added.