In the UK, the State does not own the stone on British shores, the stone is owned by the landowner. A licence is not required to extract stone, however, planning permission is required to harvest stone, and this permission will take into account safety and the environment. (ref) Meaning local stone is more likely to be environmentally friendly.
The world is full of quarries, the areas which mine resources, and one of these mined resources is stone. All over the world, different stones are harvested from different countries, meaning stones can be sourced locally and also overseas, (which may be problematic when considering the carbon footprint of imports). However, stone is various and different areas are known for different stones, for example, India is known for strong and durable sandstone and the UK for its slate.
Yet despite this, there is hardly any research on the environmental impacts of specific quarries or specific countries. Quarrying can degrade environments, polluting areas nearby or destroy entire mountains, (ref), (ref) and they can also use children as a labour source. (ref) However, after days of researching, there was surprisingly little data. There is such diversity in this matter because different territories adhere to different standards in regards to the environment. The sheer diversity of quarries around the world and the lack of data on them makes it hard to advise on the sustainability or environmental impact of specific stones, be that marble, sandstone, granite, limestone etc.
Despite this, there are some ways to ensure stone has been harvested in an environmentally and ethically sustainable manner. This is through third party certification. Organisations such as ISO (International Organization for Standardisation), (ref) Fair Stone (ref) and the Natural Stone Council (ref) all offer certifications allowing a consumer to know the standards in which the stone was harvested.
Some companies also provide information about the environmental costs of transporting stone into the UK, one example being Marshalls who provide a carbon calculator for their products. (ref)