The Ethical Consumer Research Association has published this guide and has ranked the top designer labels according to their Corporate Social Responsibility. There was not one shining star with at least somewhat good CSR. The highest ranking given was a 7 out of 20 (pretty bad) to companies like Alberta Ferretti and Jean Paul Gaultier. The lowest were Marc Jacobs and Louis Vuiton with 1.5. A questionnaire was sent to all companies about their CSR all of which declined to fill it out.
According to the report some of the fast-fashion companies have better CSR in place that these luxury companies mainly because pressure has been put on them to clean up. Luxury brands however have been able to elude criticism mainly thanks to reputations established years ago around high quality, crafted items, when in reality most are produced in China or a similar low-cost country.
You can also download for free the Deeper Luxury report.