As with several other shoppers, Ms Bui noted the impact of rubbish particularly in the oceans, recalling a video she recently watched of a whale dying after consuming plastic.

“We’ve definitely seen a shift that customers would like to [have] more sustainable options," Mr Cullen said. A survey of 12,500 Woolies customers found 74.7 per cent in favour of removing the grey plastic bags from stores, and just 14.8 per cent against.

With Coles following suit on July 1, all the major supermarket chains will have ditched single-use shopping bags by next month.

Smaller rivals IGA will complete the phase-out by the end of this month, Harris Foods has been offering alternatives since January, and Aldi has never given out free thin-plastic shopping bags.

"You've can be very sure [the big two chains] have had a very strong message from customers," Jeff Angel, executive director of the Total Environment Centre, said. "They have seen where public opinion has gone."

Karthik Venkatesh, a financial officer at Unilever, was another customer at ease with the bag phase-out.

Aldi "has had this for a very long time", Mr Venkatesh said after leaving the Woolies store in Sydney. "It's an important issue - sustainability and taking care of the environment, so that future generations will be able to enjoy what we have now."

"We are committed to protecting the environment and minimising our impact wherever we operate," an Aldi spokesman said. "It’s why all our stores have been completely free of single-use plastic bags since we opened in 2001."

Woolworths' Mr Cullen said the phase-out of plastic bags "was about doing the right thing, not about making money".

The bags were "just the start of the journey", with the company looking at 80-odd initiatives to reduce plastic packaging, he said.

A trial of Woolworth's Redcycle recycling of plastic at 100 stores in NSW and Victoria would be rolled out for all of the firm's 1000-plus outlets nationwide so customers can return "scrunchable plastic".

About 300 tonnes of material had already been collected, some of which had been recycled into benches and other furniture. Some items have been donated to schools.

“It would have gone to landfill because it can’t be recycled from kerbside [bins]," Mr Cullen said.

Josh Frydenberg, the federal environment and energy minister, welcomed the move to ban light-weight, single-use plastic bags in much of Australia.

“The Turnbull government supports state and territory governments to develop regulatory and other approaches to encourage recycling and reduce the impact of waste on the environment and human health," he said.

“Industry-led approaches, however, can be successful, as demonstrated by our phase-out of microbeads in cosmetic and personal care products.”