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Under the Occupiers Liability Act 1984 you owe a duty of care to trespassers on your land to ensure it is safe when in your property, although the duty is not as onerous as a duty owed to a visitor
With regards to the tree given you are aware of the danger that exists surrounding the tree, thus you are leaving your self open to a claim against you by a trespassers under the Occupiers Liability Act 1984.
Therefore I suggest you take proactive measures to ensure the tree is not a danger to both visitors and trespassers.