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.
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Armed police have carried out a raid apparently linked to Wednesday's deadly terror attack in Westminster.
Cheryl Grimmer vanished from inside a beach shower block in Wollongong, Australia, in 1970, when she was just three.
Pc Keith Palmer was on the front line and because of his actions, the Westminster attacker was unable to kill anyone else.