You have entered into a new 6 month agreement and that is a contract that is binding on both parties. Unless it is specifically written into the agreement that you could break it early, then you are bound by its terms for the full six months - just like any other contract you might enter into.
If the landlord or agent is willing, at their discretion, to let you break the contract without penalty, then that is entirely up to them. I don't think that on the basis of what you have said the landlord / agent has acted unreasonably. If the house had more serious issues that they hadn't dealt with or if the promised something (as part of your agreeing to the let) which they didn't deliver then you might have an argument.
If I were you I'd go back to the agent and attempt to resolve your housing problems with them i.e. see if they or the landlord they act for have another property you could take. Alternatively, wait 4 more months, then give your months notice and find another place.