The proposal is part of the mayor's target to increase the amount of waste sent for recycling by 50 percent, The Times of London reported Monday.
"If all U.K. shoppers cut out just one in five bags, it would save about 40,000 tons of CO2 equivalent greenhouse gases a year -- equivalent to taking over 12,500 cars off the road for a year," Johnson said.
Incentives will be given to shoppers to use reusable bags and supermarkets will be encouraged to place a charge on bags they provide at checkout, The Times said.
The mayor says he knows by example rapid progress can be made to cut the 13 billion plastic bags given to consumers in Britain every year.
The Times reported Modbury in Devon became England's first plastic-bag-free town in 2007.
When the Republic of Ireland started charging customers 15 cents per bag in 2002 plastic bag use dropped 90 percent. In 2008 the average Irish consumer used 27 bags contrasted with Britain's 220 per person.