A consultation on the plan to set a minimum price of 0.45 pounds per unit of alcohol closed last month, the measure meant to help tackle anti-social behaviour but which critics said punished responsible drinkers and the poor.
British media outlets said the plan was dropped due to government divisions on the issue, but cited no sources.
The proposal also reputedly was opposed by the Treasury due to its likely negative impact on tax revenues at a time of strained public finances.
A spokesman for Prime Minister David Cameron's office declined to comment on the reports.
"We've consulted on proposals on minimum alcohol pricing, and the results of that consultation will be announced in due course," the spokesman said.
The plan's cancellation could trigger a backlash by health campaigners and people affected by heavy drinking in urban centres, where problems arising from cheap alcohol have strained medical and police services.
A unit is defined, in Britain, as 1 centilitre of alcohol. A 0.5 litre can of beer with a 5 percent alcohol content has 2.5 units.
(Reporting by Mohammed Abbas; Editing by Michael Roddy)