Less than two years after the law was changed to force large stores to charge for them, the supermarket giant is looking to end the sale of so-called 'single use' carriers.
See also: Is this Britain's oldest carrier bag?
Once gone, customers who forget to bring their own bags will have to fork out 8p or 10p for a 'bag for life' instead, said Tesco.
Tesco, Britain's biggest retailer, is launching a ten-week trial in three stores to see how customers get on without the 5p bag option.
If successful, it will be rolled out nationwide - which will inevitably spark supermarket rivals to do the same if they want to boost their green credentials.
And the signs are that it will work.
Tesco says that in the last year alone, the number of 5p bags it sells has fallen by 72 per cent in stores.
Since the law change for English stores in October 2015, Tesco has handed out 1.5 billion fewer bags than it would normally have done over the same period.
The plastic bag charge was introduced to cut down on the use of the plastic bags which are not recyclable, ending up in landfill as well as being a litter menace.
Online shoppers also have the choice of the 5p bags or no bags at all and 57 per cent now choose bagless deliveries but the initial trial is simply in stores in Norwich, Aberdeen and Dundee.A spokeswoman for Tesco told trade journal The Grocer that the trial was intended 'to look at the impact on bag usage if we remove single-use carrier bags.
"In these stores, customers who need a bag can still buy a bag for life, which they can reuse," the company said.
Money raised from the sale of the 5p plastic bags goes to community groups involved in green projects and Tesco has donated £72 million so far.
The retailer said it will carry on backing them.