The charge will come into effect in autumn 2015, after the next general election, and will bring England into line with other parts of the UK.
Charges are already in place in Wales, where there has been a 76% fall in plastic bag use since it was introduced in 2011, and Northern Ireland, with Scotland to follow suit next year. The charge has been in place in the Republic of Ireland since 2002.
The charge will only apply to supermarkets and other large stores. Small corner shops will be excluded.
The proceeds will go to charities involved in clearing up the environmental damage caused by the bags rather than the government or the retailers.
The energy and climate change secretary, Ed Davey, said the plastic bag levy would only raise "pretty small amounts" for charity as its aim was to get people to cut the number they use.
"It is a huge environmental step forward. Liberal Democrats in this coalition government have been championing the green agenda," he told the BBC. "One of the great things about this charge is the government is saying 'try to avoid it'. We want you to not pay this charge by reusing and not using plastic bags.
"The success of this charge will be that it doesn't raise any money. We are very clear that none of this money will come to government; we are not trying to tax people, we are trying to change people's behaviour, encourage much more environmentally friendly behaviour."
However, environmentalists said the bag levy was not enough to improve the government's poor enivironmental record.
Friends of the Earth's policy and campaigns director, Craig Bennett said: "A plastic bag charge is welcome news, but let's not get carried away. This small step will do little to tackle the nation's huge waste mountain and can't disguise the government's woeful green record.
"Tougher action and ambitious targets are needed to cut waste and boost recycling, and bring England in line with the rest of the UK and much of Europe.
"If Nick Clegg wants to champion the environment he must do much better – starting by allowing Lib Dem peers to back a 2030 target for decarbonising the power sector when the energy bill reaches the House of Lords."
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Plastic Bags: Shoppers To Be Charged 5p - Sky News, 14-Sep-2013
