Sources close to the coalition government have revealed to the media that Chancellor George Osborne will announce the scheme will be scrapped when he delivers his Budget speech.
Education minister Michael Gove and former health secretary Andrew Lansley are also said to have opposed the scheme.
Last week London Mayor Boris Johnson joined in, calling the plans “regressive” and warning they would punish moderate drinkers and the poorest of our society.
The WSTA welcomed the speculation, adding: “Minimum unit pricing would penalise responsible drinkers and treat everyone who is looking for value in their shopping as a binge drinker.”
But Conservative MP Sarah Wollaston, a former GP who has led the charge for minimum unit pricing, said she was “devastated”.
“This policy is about getting rid of the alcohol that’s being retailed around 22p a unit – that’s the alcohol that’s killing people and causing carnage,” she said.
Dr Vivienne Nathanson, of the British Medical Association, added a message for Cameron: “Be courageous: this is a once-in-a-lifetime opportunity to save lives, to save the country money. Both of those are very good deals for him.
“And it will get him the thanks of an awful lot of people. Not just doctors and nurses but also the families of problem drinkers who desperately want the government to do something to help them help the people they love to kick the habit and to save their lives.”
Labour MP and shadow home office minister Diana Abbott waded in to accuse Cameron and May of “weak leadership”.
She said: “The home secretary and the prime minister said this measure would cut crime and prevent alcohol abuse. What's changed?
“Both times the government announced this measure we made clear there needs to be a package around alcohol abuse, a minimum price is not a magic bullet.
“And there needs to be a clear plan to prevent a windfall for supermarkets. Both times the government insisted a minimum price was the only way forward. Theresa May has taken her eye off the ball recently. On a flagship policy this is a humiliating climbdown.”