She suggested fruit, vegetables and other fresh foods should be sold loose instead of in plastic packaging and said the United Kingdom government will work with supermarkets to encourage them to introduce plastic-free aisles in which all food is loose.
"The UK government rightly stopped the supermarkets from offering plastic carrier bags for free and they also have the power to stop retailers from offering fruit and vegetables pre-packed in plastic packaging, which is not necessary and causes pollution", the petition states.
The Bill, which the Government voted against a year ago, also seeks to introduce a deposit refund scheme on drinks containers and a deposit-return scheme for plastic bottles.
Mrs May is expected to unveil plans to extend the 5p plastic bag charge to all small shops.
Launching the document, May put particular focus on strategies to reduce plastic-related waste - saying 8.3bn tonnes had been produced since the 1950s, with the figure likely to rise to 34bn tonnes by 2050.
The prime minister described plastic waste as "truly one of the great environmental scourges of our time". Much of this waste ends up in waterways and oceans, May said, with one in three fish caught in the Channel containing pieces of plastic.
"Today I can confirm that the United Kingdom will demonstrate global leadership".
Fire reported on top floor of Trump Tower
A fire has broken out on the roof of the Trump Tower building in Manhattan, the New York Fire Department has confirmed. Fire officials said a civilian was treated for serious injuries and a firefighter suffered minor injuries.
In the United Kingdom alone, the Marine Conservation Society found 718 pieces of litter for every 100-metre stretch of beach surveyed in its Great British Beach Clean Up. We must reduce the demand for plastic, reduce the number of plastics in circulation and improve our recycling rates, ' she will say in extracts released before the speech.
At Tuesday's cabinet meeting, the prime minister "said the government had a clear belief in "conserving what is good, and standing against the profligate use of resources - whether it be public money or natural resources", her official spokesman said. "To tackle it we will take action at every stage of the production and consumption of plastic".
Friends of the Earth CEO Craig Bennett said: "A 25 year plan is clearly needed - but with the nation facing an accelerating environmental crisis we can't afford to wait a quarter of a century for urgent action to tackle the issues that already threaten our lives, health and planet".
It's become a hot topic among environmentalists and it's not hard to see why: each year the United Kingdom throws away millions of the cups, which are extremely costly to recycle due to their plastic lining.
He also confirmed that he is working with International Development Secretary Penny Mordaunt on using the £13 billion foreign aid budget to tackle the tide of plastic poisoning the world's oceans. Before the levy, the Government had estimated that 1.2 billion plastic bags were being given out free every year.
"If such usage is not to be exempted then we urge government, in line with Food Standards Agency advice, to ensure the public is fully aware of the need to use a fresh clean bag when carrying ready to eat food", said Martin Kersh, executive director of the FPA.