The AHA said that while minimum unit pricing would help protect future generations it was not a "silver bullet".
There should be a 40p minimum alcohol unit price in England and Wales to stop binge-drinking on cheap drinks, the Government's alcohol strategy suggests.
Scotland has already agreed a 50p per unit rate, due to take effect next April, but subject to a legal challenge by the scheme's opponents.
In a letter to The Sunday Times, the AHA, wrote: "This policy will tackle head-on the problems caused by cheap drink, not only to drinkers but to those around them - the innocent victims of alcohol harm.
"Minimum unit pricing will target the heaviest drinkers: those who cause the most damage to themselves and others."
It added: "A child who lives with a problem drinker is vulnerable to neglect, violence and abuse, and a significant number of child protection cases are linked to alcohol.
"It is essential that the government stands firm in tackling problem drinking in order to turn the tide of alcohol harm."
A group of leading medical organisations has called for the Government to set a minimum alcohol price of 50p per unit.
The Alcohol Health Alliance UK (AHA) said the move would tackle "head on" the problems caused by cheap drink and protect the next generation.
The AHA want to see a minimum unit price tariff target the heaviest drinkers who harm themselves and others around them, especially children.