Responsibilities of a landlord

Earlier on this year one of the 25 foot Palm Trees in my garden was blown down in the high winds, luckily this Palm Tree did not hit the house or do any major damage. The reason for the tree blowing down was that the inside trunk had been eaten away by some kind of insects.

At the time I raised my concern to the landlord that the other palm trees could be infected as well. A few weeks ago, I got the Palm Trees cleaned and one of the other trees has had half the trunk eaten away by insects. Now this tree could also potentially fall down in high winds.

I have asked the Landlord if he could arrange for taking this tree down and remove it, but he says this is covered under garden maintenance and it is my responsibility.

I must admit I was quite surprised that the Landlord took this attitude, as the tree could potentially fall on his property or the neighbours!

Please let me know in cases for removals of trees from the garden, who is responsible for this, the Landlord or the tenant?