Gordon Brown has promised to crackdown on alcohol sales to teenagers, while the government is told that the availability of alcohol full stop is the real problem.
The prime minister has vowed to shut down any shop caught selling alcohol to under-18s more than once.
The warning comes as council leaders argue the government's 24-hour drinking experiment has been a "catastrophic mistake".
Speaking to the Daily Mirror, Mr Brown said: "One thing that worries me most is the number of shops and off-licences selling to people under 18.
"We have to tighten up the penalties. Any shop that is selling to under-18s twice in three months should lose its licence. At the moment it is three sales in three months but we have to go further."
He said anyone selling alcohol to under-18s is fuelling the problems associated with binge drinking and giving young people "the worst possible start in life".
The "two strikes and you're out" rule will affect off-licences, corner shops and supermarkets and is designed to prevent young people getting hold of alcohol which they later drink in public.
Mr Brown reiterated his belief that "binge drinking is unacceptable".
As well as looking at how young people obtain alcohol, the government will also attempt to deter them from binge drinking with renewed public health campaigns, as well as warnings targeted at teenage girls about what alcohol can do to their looks.
The government is also this week expected to publish its own review of 24-hour licensing, but ministers believe round-the-clock availability of booze is not the problem per se.
Sir Simon Milton, chair of the Local Government Association (LGA) said, however, the hope that all-night licensing would end binge drinking had failed.
Speaking to the BBC he said: "The real problem about alcohol violence going later into the night is not simply to do with the clock.
"First of all if you are a resident who's disturbed at night and it's three o'clock in the morning, your chances of getting back to sleep after that are much less," he said.
"But also policing resources are being stretched further into the night."
The World Health Organisation currently rates Britain worst for drunkenness among 11- to 13-year-olds.