The Bishop of Southwark Christopher Chessun pointed to academic research that showed the top 30 per cent of drinkers consumed 80% of all booze.
He also pointed out much of the beer in supermarkets was sold on promotion, priced well below 50p per unit.
He pressed the Government in the House of Lords as a study found supermarket beer is almost 188 per cent more affordable today than it was 30 years ago.
The Scottish Government has confirmed it will set a minimum price for alcohol of 50p a unit from May 1.
The bishop said: “Does the minister agree that a floor in the unit price of alcohol would help yield a more orderly, content and healthy society by bearing down on demand?”
Health Minister Lord O’Shaughnessy said a system was needed to target those drinking “in a way that is very, very deleterious for their health”.
He told peers: “Minimum unit pricing remains under review and the Government will consider the evidence of its impact once it is available.”
He said: “I think the issue here is not about the lack of evidence about whether reducing drinking has health benefits. It’s making sure any new system is implemented in a way that is fair on those who drink sensibly, particularly those with low income.”
Lord O’Shaughnessy pointed out the tax system had been “judiciously” to target problem high-strength drinks such as white cider.
Tory peer and surgeon Lord Riberio said liver disease, unlike cancer, was the only major cause of premature death that had increased since 1970.
He called for talks “to discuss what we can do in this country to follow the Scottish lead”.
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Introducing minimum alcohol pricing would help create “a more orderly, content and healthy society”, a senior church cleric has argued.