Posting on Twitter this evening, Totnes MP Sarah Wollaston - a former GP - wrote: "Very concerned about suggestion that minimum pricing to be dropped from alcohol strategy."
Fellow Conservative Tracey Crouch said: "I really hope rumours of u-turn on minimum unit pricing for alcohol are not true. We must tackle problem of easily accessible cheap alcohol."
But Miles Beale, chief executive of the Wine and Spirit Trade Association, said consumers would welcome the move.
He said: "Minimum Unit Pricing would penalise responsible drinkers and treat everyone who is looking for value in their shopping as a binge-drinker. Evidence has also shown it will do little to tackle problem drinking."