More than two thirds of consumers want brands to do more to reduce waste.
A study of 2,000 adults found 59 per cent are 'disappointed' in the big names that still have not got their sustainability initiatives right.
And almost half feel brands are not transparent enough with their wider sustainability goals.
It also emerged one third of adults don't think brands are doing enough in general when it comes to helping the environment.
Shweta Harit, from Evian Global, which commissioned the research to mark it's achievement of B Corp status, said: "If our findings are anything to go by, it's clear that, quite rightly, there is strong appetite among consumers for greater transparency in the way brands look to create positive impact across people and planet.
"Today's B Corp announcement and our commitment to brand transparency are huge milestones for us in our sustainability journey and broader commitment to doing business the right way."
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The study also found when it comes to individual's own shopping habits, 37 per cent feel they are doing enough for the environment.
But almost two thirds (64 per cent) admit they could do more to become a better 'sustainable shopper'.
And 53 per cent would be more likely to change their own environmental habits if brands did more to change theirs.
The top actions Brits would like to see companies do more, include producing biodegradable packaging (55 per cent), easily recycled products (64 per cent) and reduction of greenhouse gases in production (36 per cent).
The use of sustainable materials in products (47 per cent), promoting environmentally friendly ways of working (36 per cent), and signing up to sustainability initiatives (31 per cent) were also on the list.
The study, conducted via OnePoll, found 53 per cent said companies are not doing enough to help them become better shoppers.
As the consumer, 73 per cent feel they are only able to buy what is available to them and it is therefore up to the brands themselves to provide more sustainable choices.
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Katie Hill, CEO at B Lab Europe, said: "We are delighted to welcome Evian to the B Corp community.
"This global movement of nearly 4000 companies from over 70 countries and 150 sectors is helping to change the way business operates, and in so doing, they redefine the qualities of success in business.
"Evian's commitment to circularity in its operations, and the transparency with which it will share this progress towards this goal, will inspire other companies to follow suit.
"Now more than ever, it is crucial for both companies and individuals to operate for the benefit of all and use business as a force for good."