Environment Secretary Michael Gove has already stated he wants to provide a "green brexit" and that "trees are some of our most cherished natural assets and living evidence of our investment for future generations".
The 5p charge on plastic bags is set to be enforced in corner shops and other small retailers, as the government extends its plans to tackle "throwaway culture".
At a Cabinet briefing on Tuesday the Prime Minister said she wanted her Government to take a stand against the "profligate" use of natural resources as she discussed a new 25-year Environment Plan.
Currently, all retailers in England with more than 250 workers are legally required to charge at least 5p for plastic bags, and donate extra proceeds to charitable causes after new measures were introduced back in 2015. In addition, he is said to be considering plans to tackle disposable coffee cup waste, although it remains to be seen if he will embrace the Environmental Audit Committee's recent recommendation for a 25p "latte levy".
A separate proposal to introduce plastic bottle deposit return schemes in supermarkets is not ready to be announced yet.
Announcing a consultation on removing the remaining exemptions, Mrs May will say that the tax shows the effectiveness of well-judged state intervention.
Michael Gove told colleagues the introduction of the 5p charge on single-use plastic bags had contributed to a reduction of almost 90% in their use, in a clear demonstration of what can be achieved by targeted official action.
The committee of MPs said the industry should be given five years to make the cups easy to recycle or face an outright ban.
One option on the table would be for the charge to be extended on a voluntary basis, the source said.
Together, the two measures are meant to ensure that a greater proportion of the packaging used in the United Kingdom can be recycled.
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