You are not responsible for this repair - the Landlord is.
Indeed, if you went ahead and hired a tradesman to do it and paid him and did this without the written agreement of the landlord you might be held liable for the costs of any subsequent repairs in the same area. Even worse if you did it yourself or had a friend do it.
Write a letter to the landlord or his agent - keep a copy - ask for it to be fixed - point out any short or long-term damage that the leak may be causing to his property and any affect it may be having on your own goods.
The leaking water may be coming from another property not belonging to your landlord - if you mess around you could have two landlords on your back for compensation.
You certainly have a moral obligation to tell the landlord of any defect that might be damaging his property and may also have a legal obligation to tell him too.
Good luck...
Peccavi
August 2009