The government has come under pressure to follow Scotland’s lead, which has proposed ₤0.50 (€0.62).
The minimum price will reduce the ₤42 billion (€52 billion) a year spent on alcoholic beverages in England and Wales by just over 3% but could curb crime and prevent 714 alcohol-related deaths each year, Britain's Home Office has said.
It is also considering banning offers such as ‘buy one, get one free’.
The Home Office said the consultation was targeted at "harmful drinkers and irresponsible shops".
A spokesman added: "Those who enjoy a quiet drink or two have nothing to fear from our proposals."
The ₤0.45 minimum would mean a can of strong lager could not be sold for less than £1.56 (€1.92) and a bottle of wine below £4.22 (€5.23), BBC reported. Some cheaper supermarket beers and spirits could double in price.
'Paying a heavy price for misuse'
The ₤0.45 proposal is ₤0.05 higher than ministers proposed in March, but to some campaigners it is not enough.
Alcohol Concern's chief executive, Eric Appleby, said: "We're paying a heavy price for alcohol misuse and setting a minimum unit price will help us on the road to changing this.
"Evidence shows us that setting the unit price at 50 pence will have most impact on those vulnerable groups we must protect: the young and heavy drinkers."
The Home Office said it would also have to assess the impact of shopping from Scotland if the two proposals were to go ahead.
Industry groups such as the Scotch Whisky Association and the European Spirits Organisation have claimed minimum pricing may be incompatible with European Union trade rules.
By contrast with minimum pricing, French ministers have proposed to increase tax on beer by 120%, a move which could increase the price of a half-litre by 30 to 40 cents.
Malta and Spain are the cheapest places in Europe to buy a beer and wine respectively, according to a direct comparison of prices by the Institute of Alcohol Studies (IAS).