Health campaigners are asking for more substantial rises in cigarette duty in this month's Budget.
Chancellor George Osborne is already committed to increasing duty by 2% above inflation.
However, a submission signed by 91 organisations argues this should rise to 5% - about two pence per cigarette.
Smokers' lobby groups are already fiercely opposed to the 2% rise, and warn people would turn to smuggled and counterfeit cigarettes.
But campaign groups such as the UK Centre for Tobacco Control Studies (UKCTCS) and Action on Smoking and Health (ASH) say that despite years of rising tobacco duty, increases in disposable incomes mean that tobacco remains relatively more affordable than it was in the 1960s.
Their call for a move to a 5% "escalator" were rejected by the chancellor last year.
Prof John Britton, director of the UKCTCS, said hitting smokers in the pocket was the best way to get them to stop.
"Price is the most effective way to encourage smokers who are thinking of quitting to make that step," he said.
"UK cigarettes are more affordable now than they were when the health risks of smoking first became known.
"It is crucially important to use the price levers to nudge smokers to change."
Deborah Arnott, chief executive of ASH, said the tobacco industry was trying to "undermine" anti-smoking measures, arguing that higher tax, and calls for standardised plain packaging for cigarettes would lead to more smuggled tobacco.
"As ever the industry is clutching at straws with its ill-founded arguments," she said.
The campaigners are also calling for more duty on hand-rolled tobacco to stop smokers switching to save money, further action to curb smuggling and even moves to force tobacco retailers across the UK to be registered.
However, Simon Clark, from Forest, the smokers' lobby group, said that a 5% increase above inflation would produce an "economic madhouse", and cause an explosion in smuggled and counterfeit cigarettes.
He said: "Ideally we'd like to see a reduction in duty, but the next best thing would be a freeze on tobacco duty, so that's what we're hoping for."