NFWI, which also launched a campaign targeting the anti-competitive behaviour of big name grocers last year, claims more than 88,000 tonnes of weekly household waste - 4.6m tonnes per year - is generated from groceries and their packaging.
As a result, the group recommends axing unnecessary packaging, using only compostable and recyclable materials, charging consumers for plastic bags and donating waste to food charities or composting sites.
It is also pushing for more transparency in the system, urging supermarkets to publish packaging and food waste strategies.
The campaign, launched on 20 June, has been backed by government ministers, celebrities and The Ecologist magazine.
"WI members want supermarkets to reduce unnecessary packaging and put the environment first. I urge the public to join our campaign and return unnecessary and excessive packaging to supermarkets," said NFWI chair Fay Mansell.
"Climate change is one of the biggest threats facing our world today. Supermarkets must take action now to reduce the packaging which, as landfill waste, releases greenhouse gases," she added.
But the Industry Council for Packaging and the Environment (INCPEN) said packaging prevents more waste than it generates.
If goods are damaged or spoiled, far greater energy and materials go to waste. Also product damage caused by inadequate packaging causes major consumer complaints, according to the INCPEN.
"Packaging plays an essential role in sustainable distribution, ensuring goods are delivered safely from producer to consumer," it said.
It claims there are a number of drivers pushing companies towards continuously improving packaging, including two UK laws, EU guidelines and various sponsored green supply chain initiatives, but has called for an independent packaging watchdog to assess performance and allay public concerns.
The INCPEN said much has changed since the 1990s, as more retailers and suppliers strive to cut packaging volumes and substitute biodegradable materials where possible. Glass containers are now 30 per cent lighter than in 1980, while carrier bags are 45 per cent lighter than 1990.
The Waste Resources Action Programme (WRAP), a not-for-profit organisation funded by the British government, has been working with retailers on the issue of packaging reduction.
It encourages companies to tap into its £8million (€11.8m) innovation fund to reduce packaging, production and transport costs and encourage corporate social responsibility gains.
So far thirteen retailers have pledged interest in the scheme, including Asda, Sainsburys, Marks and Spencer, Morrisons, Tesco and Waitrose, and global manufacturers such as Heinz are also benefiting from the "green grants".
WRAP said these initiatives are starting to filter down through the industry, but it welcomes the work of the WI in highlighting its cause.
Currently around half of UK household rubbish, which ultimately ends up in landfill, originates from supermarkets and convenience stores, according to WRAP.
With a gross output of £65.7bn, the food and drink business is one of the largest sectors in UK industry, accounting for 17 per cent of manufacturing GDP.
"The food and drink sector produces about seven million tonnes of waste per year, most of which is food waste - making it the biggest manufacturing producer of industrial waste," said an Environment Agency spokesperson.
"And this number is growing by around five per cent per year," she added.
But under EU law, the UK must half the amount of waste going to landfill by 2013. And failure to comply with the regulations could mean fines running at half a million pounds per day for the British government.