If there is no existing designation, but you believe that the site is highly valuable for wildlife or other conservation interests, then you can try lobbying for its protection. Do bear in mind though that getting a site designated is not usually a quick or easy process and you will need to be able to clearly demonstrate that the site meets the relevant criteria for statutory or non-statutory (local) site designation.
To start, you will need good quality, scientifically gathered evidence of the species or other special features present on the site. Ideally, you will also need strong support from local wildlife organisations and the local Ecologist or Biodiversity Officer (if there is one) within the local authority. National designations including SSSIs/ASSIs are the responsibility of the statutory nature conservation bodies (ie Natural England, NatureScot, Natural Resources Wales, Northern Ireland Environment Agency), while local designations are generally the responsibility of the relevant local authority.
It is also a good idea to speak to the landowner if you know who they are. Remember that you will need the landowner’s permission if you wish to carry out wildlife surveys on their land away from public footpaths or other permitted access areas.