Gant

This company has announced that they don't sell animal fur or are phasing in a fur-free policy.
[Source 2014][More on Animal Rights]

This company is a member of the Better Cotton Initiative, a voluntary initiative which encourages the adoption of better management practices in cotton cultivation to achieve measurable reductions in key environmental impacts, while improving social and economic benefits for cotton farmers, small and large, worldwide.
[Source 2019][More on Multi-Stakeholder Initiatives]

This company has a number of corporate responsibility claims on its website covering the areas of code of conduct, chemical use and water use.
[Source 2013][More on Sustainability Reporting]

This company is a member of the Textile Exchange, a global non-profit that works closely with its members to drive textile industry transformation in preferred fibres, integrity and standards and responsible supply networks. They identify and share best practices regarding farming, materials, processing, traceability and product end-of-life in order to reduce the textile industry's impact on the world's water, soil and air, and the human population.
[Source 2019][More on Multi-Stakeholder Initiatives]

California, the UK and Australia have all enacted legislation requiring companies operating within their borders to disclose their efforts to eradicate modern slavery from their operations and supply chains. Follow the link to see this company's disclosure statement.
[Source 2018][More on Human Rights]