You might also want to check whether letting agents belong to association - used to be ARLA - not sure if still is. You could check with them re your rights v letting agents. I used to be both landlady and tenant, so have experience of both sides - as landlady, my letting agents didn't always pass on details of problems, so don't necessarily take everything letting agent says as gospel.
If damp is a problem with asthma, does Slugsta Jnr have a friendly GP who'd sign some form of medical document saying this is the case, so that you can use it to exert extra pressure?
You need to get exact time frame from letting agent, otherwise it will just fester.
Re notice, you'd need to check, but if flat is not "fit for purpose" as said above, then I think that would negate contract, but, from memory, most insist that you remain in (or pay rent for) accommodation for at least first 6 months on 12 month contract.
If you can get your hands on contract, you should also be able to see who is responsible for repairs etc, it's not always the agent, sometimes they just collect money, check references etc and leave repairs to landlord (as landlord often thinks it's cheaper than getting agent to fix).
Whatever action you take, put it all in writing - whether email or letter - that way you've got a record of what was said/agreed and by whom.