It is strongly advised that you report your sighting to the police and to be careful when reporting to the press/media. The police need to know that cat sightings are being made in your \ their area so that they can collate this information and act accordingly. There will be a police Wildlife Liaison Officer that you can contact who is usually responsible for these and other countryside matters. No matter how anxious you may feel in talking to the police (some forces are very supportive others are not) it is important they know what is happening; so please contact the relevant Police Wildlife Liaison Officer.
Press/media involvement can sometimes be proplomatic dependent upon who you are dealing with. Sometimes they wish to embellish events with the result of much unhelpful publicity for individuals & communities. Other times reporting is accurate and informed. However, if you feel that they should be contacted please consider talking to the police and seeking their advice on your sighting/event as they are often aware of other issues relating to individual cases. They may/may not suggest keeping press/media involvement to a minimum; or they may not.
DEFRA ( Department for Environment & Rural Affairs)
DEFRA have the widest remit possible for countryside matters. They should be a valuable tool in the search for non-native big cats....however, to date I have found it hard to locate any department within the organization which deals with Big Cat sightings specifically. Notwithstanding this, if you go to their website http://www.defra.gov.uk/ and go to the search bar and type 'Big Cats' a number of documents appear on the subject (so someone somewhere or on DEFRA's behalf does at least collate information on big cats ). I would advise that any attacks on wildlife that you suspect could be the work of a Big Cat or dog should be reported to DEFRA. Sadly, like the police DEFRA can sometimes be supportive other times not.