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.
Commenting on the plan, EIC executive director Matthew Farrow said:"Prime Ministerial speeches on the environment are an endangered species, so it is very welcome to hear Theresa May emphasise the crucial importance of the environment, the number of green jobs, the interdependence of economic growth and environmental progress, and the scourge of plastic waste".
The Change.org petition recommended that supermarkets offer brown paper bags instead of clear plastic bags in the fresh produce aisles, and use cardboard punnets for smaller items like berries instead of plastic ones.
Shoppers who shun plastic packaging could skip busy supermarket queues under proposals put forward by Theresa May.
May said: "In years to come, I think people will be shocked at how today we allow so much plastic to be produced needlessly". This is 9kg more than the second worst offender, Luxembourg.
The Government will also look at how the tax system or charges could further reduce the amount of waste with media reports suggesting a tax on takeaway containers was being considered.
As a final point, it's worth noting that some coffee shops, such as Pret a Manger, already offer a discount of up to 50p if you bring your own coffee or tea cup in with you.
Mr Gove, who showed off his new reusable coffee mug as he walked into No10 yesterday, is also expected to announce measures to cut the 2.5billion disposable coffee cups wasted in the United Kingdom every year.More news: Donkey Kong Country: Tropical Freeze Coming to Switch
The Bill, which the Government voted against previous year, also seeks to introduce a deposit refund scheme on drinks containers and a deposit-return scheme for plastic bottles.
"According to the United Nations, eight million tonnes of plastic leak into oceans each year", the Waterford Senator added.
Under the pledge waste such as the carrier bags, food packaging and disposable plastic straws that litter the country and pollute the seas would be abolished.
There are also concerns about the potential impact on food chains.
In November 2016, then Minister for Housing Simon Coveney wrote to the European Commission to inform them of the Government's plans to introduce legislation banning microbeads in 2017.
Helen Munday, its chief scientific officer, said: "We look forward to studying the details of the plan, and hope that it will sit alongside the industrial strategy in the creation of a long-term framework in which businesses can operate".
In a question and answer session after her speech, Mrs May didn't rule out a deposit return scheme for plastic bottles, saying "what matters is what works" and she recalling a time when she used to return Corona bottles for a "sixpence".
Liberal Democrat leader Vince Cable said the Prime Minister had shown a "complete lack of ambition", adding: "The Conservatives should be eliminating all avoidable plastic waste now - a target of 2042 beggars belief".