Under the Conservative proposal, a four-pack of extra-strong lager would cost around Ģ1.30p extra and alcopops would be 50p more expensive per bottle. But lower-strength drinks would see duty slashed.
Kebab shops and other late-night food outlets would also lose their right to sell alcohol under the plans.
Mr Cameron, who recently joined police in Hull on a fact-finding tour to look at alcohol-related crime, said that as well as the tax plans, there would be "serious changes" to the Licensing Act.
He said: "We don't want to go back to the situation where every pub shuts at 11 o'clock and everyone poured out into the market square and beat each other up - of course we don't want to go back to that - but we've now got a situation which I saw in Hull where pizza and kebab shops are selling high-strength lager and cider and whisky at two o'clock, three o'clock in the morning.
"Of course the prevalence of alcohol is only one part of the problem, but it cannot be right that the licensing system is as lax as it is. So we would change that rule. We would give the police more power to take away licences where they are being abused. Give the public the opportunity to challenge licences where they exist and they are doing harm."
Figures from the Office for National Statistics suggest 23% of men and 13% of women regularly drink more than the Government recommended level of 21 and 14 units a week respectively. But the equivalent figures in 2000 were 29% for men and 17% for women, suggesting a small reduction in problem drinking, Western Mail reported.
The Portman Group, which promotes responsible drinking, cast doubt on the Conservatives' approach.
David Poley, the Portman Group's chief executive, said: "The underlying issue is problem drinkers, not problem drinks."