Thanks for that, Ha, They have a Duty to House you in a Decent living environment, Which by tha aounds of it this property is not, also, they should have told you of the complaints the downstairs tenant makes.
I believe I read further up you have not been in the Property for long, and there is Mould, what you need to do it take photos of the Damage the Mould has done, then you need to get on to the Environment Officer, and make a complaint.
Have you been feeling unwell? If so this could be down to the Dampness in the Flat, do either of you have Asthma. as this is set of by the High Humidity in the Flat, which in turn brings on Bed Bugs which is then breathed in to the repository tracked, so you get Ill.
You say there is no no Carpet in the Flat, is it in the Tenancy Agreement for you to replace the carpet, or is that the Property of the HA.
There is only one way to Deaden the Floor, and that is to have a Acoustic Underlay Fitted, (A Proper one) not just a fit from Carpet right.
Now, what you also need to do is ask the Local council to have visit from there Environment Officer, and tell them the Noise Problem, if you are pushy enough, and the council does it job right, the Environment Officer will send in a Acousti Specialist to give sound reading. now, if the sound reading are above the Legal Limit, then the council should, and I mean Should, then write to the HA telling them the problem and they will need to get there officers out to asses the property, also, get on to your Local MP, go to their Surgery, and tell them your story, take any Photos, Dates, Time, Notes of what was said by who etc.
Dont forget to go to the Doctor and get some medication for the Stress this is causing.
The HA was in the Wrong for moving you in to this Property by the sounds of it,
Hope that helps a bit, will take a long time to sort things out, but the Doctor is the Key! & your MP, belive it or not!
Good Luck