Indeed, a duty of care is owed (many clients of mine believe initially that NO duty is owed to trespassers - I'm an insurance underwriter - but that's a dangerous assumption).
However, to even up the scales of justice, I do believe that IF negligence is proved and liability established (ie, the trespasser wins his case), the damages awarded are reduced significantly to take into account that he shouldn't have been there in the first case, although clearly, each case would be considered on its merits and particular circumstances. I've been a reluctant trespasser in the past when retrieving my spaniel and I like to think my case would be considered very differently to someone who trespassed with malicious or criminal intentions.