Amid growing awareness about climate change and a consequent shift in consumer behavior, brands are increasingly selling more sustainable goods.

From vegan footwear to recycled denim and organic toothpaste, the offer to consumers is growing — but such items are often more expensive than their non-sustainable equivalents.

"As a fair trade business and the only retailer to be certified by the World Fair Trade Organization, it is important to us that we know the true cost of the product so that the people making the goods are paid a fair price and a 'living' wage," Melanie Traub, managing director at online retailer People Tree, told CNBC via email.

"We try to educate our customer to understand this process. We are not trying to compete. We are providing beautiful clothes in sustainable fabrics at a fair price."

People Tree, which was established more than 20 years ago and is based in Tokyo and London, developed the first integrated supply chain for organic cotton. It has also sought to reduce its environmental impact, including ensuring that all its clothing is free of azo dyes, and thereby not containing any synthetic dyestuffs based on nitrogen that can have carcinogenic and allergic effects on some people.

Traub is confident that consumers understand that a guarantee of organic cotton and sustainability carries a price.

"Anyone can say they are selling organic cotton, but we can prove that we do. This comes at a cost, but the customer then knows they are paying for the genuine thing," she said.

People Tree products are sold in different countries, including in Japan, the U.K., Germany, Belgium, the Netherlands and Luxembourg. Traub said the company plans to expand into the U.S. and France. "We are seeing a large increase in traffic from the USA and realize it's time to make the product available there too," she said.