Sites of Special Scientific Interest (SSSIs) are areas designated by the government conservation agencies for protection. Some are geological, most are biological, and some are designated for both aspects. They are meant to protect the best examples of different habitats or important populations of particular species. So anyone’s land can be designated as an SSSI, whether they want it to be or not. Most nature reserves are SSSIs because the conservation bodies buying land for nature reserves are to some extent using the same criteria as the SSSI criteria. Many SSSIs are privately owned and there is not necessarily any right of access for the public. On the other hand, the huge network of public footpaths in England and Wales gives some access to many SSSIs. You won’t find SSSI boundaries shown on Ordnance Survey maps, but you can get them off websites: Lle.gov.wales for Wales and designatedsites.naturalengland.org.uk for England. I don’t find them very easy to use but that is probably my fault rather than the websites’.
But for a quick tour of UK wildlife sites, I would concentrate on the easily accessible ones - nature reserves of Natural England, Natural Resources Wales and Scottish Natural Heritage (the three British government agencies) plus the charities National Trust, RSPB and county wildlife trusts rather than trying to negotiate access to SSSIs that are not open to the public.