Speaking in advance of a report examining the performance of the Licensing Act, which introduced 24-hour drinking, Brown said "irresponsible shopkeepers" were fuelling a binge- drinking epidemic that is blighting the lives of young people.
"One thing that worries me most is the number of shops and off licences selling to people under 18," he said. "If someone is selling to under-18s, they are allowing these problems of binge drinking to grow, and they are giving young people the worst possible start in life.
"While one sale to an under-18 could be an innocent mistake, the law should no longer accept a second offence."
The Association of Convenience Stores (ACS) has slammed the two strikes rule, describing it as a "painfully obvious smokescreen" to distract critics of the government's current alcohol policy.
ACS chief executive James Lowman said: "There are myriad complex issues surrounding alcohol misuse, but instead of taking real steps to tackle them, the government resorts to mud-slinging at hard-working people in the front line of preventing underage purchases."
Lowman continued: "Making the mistake of selling alcohol to someone underage already comes with the threat of fines and prison sentences. This rhetoric does nothing but de-motivate responsible businesses who are tackling this problem."
The new rule, which will be accompanied by an increase in test purchasing stings, will form the centrepiece of the government's plan to crack down on alcohol abuse.