Whats the service level agreement between you and the Letting Agent to respond to problems?
My contract as a Landlord states the Agent will contact me if my Tenant has any problems with stuff like that, I have 24 hours to respond. In the event I dont respond in this time the Agent will respond on my behalf and make a decision on repairs etc... on my behalf.
Check your contract, and if they are in breach of it talk to them about it. If no joy go see Citizens Advice.
Ps: I know its no help now but I would never have paid a full years rent up front