Have you put your requests in writing? I think it's always best to follow up any phone call with an email or posted letter outlining what you have discussed/agreed on so that if you ever need to take things further (like small claims court) you have a clear paper trail. Photos are important too.
I like to use phrases like "health and safety implications" and "to protect all parties involved" and "if this matter ever needed to be escalated". State your timeframes ie we first contacted you about this mater on X date and it remains unresolved on X date. You can also quote the parts of your lease where it states that it is the landlords reprehensibility to fix things as well as reminding them that you are paying for a service. That service should not put your health in danger.
Contact the CAB and find out/understand your rights. If you are otherwise happy with the place you are living, it is worth getting a bit or a sue-happy american attitude on them first. It's not easy to find a good flat/house and if this works, great. If it doesn't, then you can either sue, or move on. I do think there are landlords who are used to tenants who grumble but never push for action and they will try and get away with whatever they can.
When I lived in Ealing, my landlord was amazing and fixed everything straight away. Where I live now the landlord was initially quite resistant to fixing the laundry list of stuff he had ignored for the last 8 years (according to the building porter). This included a set of blinds that was broken in the "open" position so that anyone on the street could see right into my living room. (Not cool!) I asked nicely/casually at first but when he resisted using the "I have no money" excuse, I wrote my formal email, included the pictures, and he did sort everything out. Which is good because I really had no desire to move again as it's a hassle.
Good luck with getting this sorted out!
