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Carly Griffin supports the idea but says businesses will need help
The Welsh government is pressing ahead with delayed plans to ban single-use carrier bags and plastic drinking straws in Wales.
Plastic plates, cutlery, stirrers and cotton buds would also be banned under the proposed new law.
Climate Change Minister Julie James said Wales must "avoid leaving a toxic legacy" to future generations.
The Conservatives accused Labour ministers of "dragging their heels on environmental issues".
England and Scotland have already banned plastic straws, cotton buds and stirrers.
However nowhere in the UK has stopped the sale of single-use carrier bags.
The new Welsh law would make it an offence to supply or offer to supply what ministers call "littered and unnecessary disposable single-use plastics".
The Welsh government said the law needed to bring in the changes was delayed by a complicated piece of post-Brexit UK legislation.
The bill, which will now begin the required scrutiny process before it can become law, would also give local councils the powers to enforce the ban on single-use plastic items including:
The list follows a consultation in 2020 and the Welsh government argues there are non-plastic or reusable alternatives to all of the products.
Straws can be sold by pharmacists and are allowed for medical or care reasons.
Anyone else who supplies these products could be fined, with councils having powers to raid premises.
The legal changes will allow ministers to add or remove items, provided those changes are backed by the Welsh Parliament.
In June, Ms James told the Senedd's climate change committee that she was considering a ban on plastic wet wipes.
But the bill does not include such a ban, and indicates that this could be considered in the future.
"Single-use plastic products are often seen littered in our streets, parks and seas," Ms James said.
"Not only are they unsightly, but they have a devastating impact on our wildlife and environment.
"With a Team Wales effort, we have to say no to the single-use item culture, so we avoid leaving a toxic legacy of plastic for future generations to deal with."
Wales was the first part of the UK to require retailers to charge for single use carrier bags in 2011 and the 5p charge must be given to charity.
The news has been welcomed by one business owner in Cwmbran who has said an urgent "shift in mindset" is needed.
Lauren Morse, founder of Zero Waste Torfaen, told BBC Radio Wales: "We are behind the rest of the UK on this, but we are finally here."
She continued: "I think it's mainly about getting it into people's mindsets. I think we need not only for this legislation to come through, but also a big education on it.
"It would be good to see some support for businesses who are currently still using single-use plastics, like polystyrene packaging at takeaways."
Carly Griffin, manager of the The Sage Deli in Cardiff Market, backs the idea of banning single-use plastics, but warns "you need to have the infrastructure in place to make it possible".
She said: "A lot of the time when this kind of legislation goes through it's very much, 'we're going to do this but now you guys figure it out'.
"So if it turns out, by 2023, everybody has to use recyclable materials, where do those containers come from?
"And then, the businesses already using them - are they going to be able to get their supplies, going forward?
"I think it is a good idea but as long as they go the extra mile to make sure it is possible, I guess and making it affordable too."
Ms Morse said when speaking to fellow business owners in Cwmbran, the cost of biodegradable packaging had been cited as a barrier.
Louise Tambini, deputy chief executive of Keep Wales Tidy, called the bill a "really good start".
"Plastics is a big issue that everyone is concerned about, we know that from the amount of people who raise it with us," she said.
"We all have that job now to see how we can get rid of it from our environment.
"It's now about looking at what other things can be banned going forwards, things like wet wipes.
"The new legislation that's being worked on on packaging will have a huge impact when that comes into force."
Llyr Gruffydd, the Plaid Cymru Senedd member who chairs the climate change committee, said the Welsh government was "playing catch-up with the Scottish and UK governments, which have already legislated to ban certain single use plastics".
"I've argued in the past that urgent progress needs to be made, but rushed law often leads to bad law and the Welsh government must now ensure the Senedd has the time to do it's work and scrutinise the proposals in detail," he said.
Welsh Conservative climate change spokeswoman Janet Finch-Saunders accused Welsh ministers of "damaging Wales" by "dragging their heels on environmental issues".
"The ban on the sale of single use plastics has already been implemented in both England and Scotland, while Labour ministers have now just decided to begin passing legislation," she said.
"The ban on the sale of single use plastics has already been implemented in both England and Scotland, while Labour ministers have now just decided to begin passing legislation.
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