I would post your Statements (H&S, Environment etc.) on the website and let others have the full policy on request.

There is no legal requirement to publish anything unless you are a public sector organisation, where the Freedom of information Act applies. If you are(and the definition of “public sector” is wider than just owned by the government -local or national) in the public sector will be expected to provide any reasonable information about your activities unless there is good reason not to do so. So a H&S policy would probably come under that. Of course it is not as simple as that simply publishing everything and anything. We don’t just have H&S policy but multiple policies  covering every aspect of our work, some of which we might not want  to share with Joe Public. If for example, we ran a business printing money( we don’t!) we would not be expected to publish documents about our procedures that might make it easier for someone to gain access to that lovely cash. There also requirements under other legislation not to disclose information such a Data Protection law or even the Official Secrets Act.  

Most organisations have a great deal of discretion about what they can publish, and some do, often as by doing this it promotes them as open organisations that believe in transparency. If you are doing that then it should really be something that is carefully considered as part of the company’s brand management, not just an info dump onto the internet.