The existing 5p charge is to be doubled and will no longer be restricted to large retailers.
The new measures laid out by Michael Gove come as schools are being urged to end the use of single-use plastics by 2022.
It is estimated around 3.6 billion single-use bags are supplied a year by small retailers exempt from the current 5p levy.
Trade bodies representing around 40,000 small retailers have already launched a voluntary approach to the existing charge, but this accounts for less than one-fifth of England’s estimated 253,000 small and medium-sized enterprises.
The changes, which could come into effect in January 2020, are contained in a consultation which has been launched by the government.
Theresa May announced in August there would be a consultation on changes to the plastic bag levy by the end of 2018 despite reported opposition from the Treasury and Chancellor Philip Hammond.
Mr Gove said: “The 5p single-use plastic carrier bag charge has been extremely successful in reducing the amount of plastic we use in our everyday lives.
“Between us, we have taken over 15 billion plastic bags out of circulation.
Six steps you can take to protect the environment in 2019
The UN Committee on Climate Change has warned that we have just 12 years left to save the world from catastrophic climate change.
“But we want to do even more to protect our precious planet and today’s announcement will accelerate further behaviour-change and build on the success of the existing charge.”
The 5p charge was introduced in England in 2015, with the money raised going to good causes rather than government coffers.
Nearly two billion 5p plastic bags were sold in the last financial year, figures from the government show.
This is a stark reduction from 2014, when 7.6 billion carrier bags – the equivalent of 140 per person – were handed out solely by England’s seven largest supermarkets.
James Lowman, chief executive of the Association of Convenience Stores, said: “We welcome the government’s plans to extend carrier bag charging to all shops.
“This has been shown to be highly effective at reducing waste, whilst also raising money for local, national and environmental charities.
“Around half of small shops in England already charge for plastic bags voluntarily, with wider support for a mandatory charge.”
Dr Laura Foster, head of Clean Seas at the Marine Conservation Society (MCS), said she hoped there would be support for the move.
The MCS has been monitoring the impact of the 5p charge since it was introduced in October 2015 and regularly provides evidence for government consultations.
Dr Foster said: “We are able to measure the impact of legislation and we’ve seen that since the introduction of the plastic bag charge in the UK the amount we find on the beaches has gone down.
“That’s also been replicated by studies that have been done offshore – they’ve also seen a reduction in the amount of plastic bags they find.
“So we do know that legislation can directly impact on the amount we find on our beaches and in our oceans.”
Education Secretary Damian Hinds has called on school leaders to stop using items including plastic straws, bottles and food packaging such as cling film in favour of sustainable alternatives.
He said: “On my first school visit as education secretary almost a year ago, the very first question I was asked by a pupil was what we can do to limit the damage of plastic on the environment.
“Reducing our use of plastic clearly is an important and timely issue which has captured the interest and the imagination of everyone in society.”
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Mr Hinds is urging schools across the country to follow the lead of Georgeham Primary School in Devon, which is the first in the UK to achieve single-use plastic-free status.
:: Sky’s Ocean Rescue campaign encourages people to reduce their single-use plastics. You can find out more about the campaign and how to get involved at www.skyoceanrescue.com