No, I disagree. The symptoms described do not suggest it. Been there three years with no problem, and evidence of dampness in two places in two different rooms but linked near a common wall. Also issue has occured in the back in the back end of summer - its not the dead of winter yet.
Something is quietly leaking away in there. If you are satisfied with your neighbours explanation, then it is more likely that a pipe in the floor above the area is quietly dripping.
Contacting the NHBC is a dumb idea. Once two years' are up, these policies revert to structural warranty only for the balance of time up to 10 years in total. They will not deal with it.
You are going to have to work through the HA, as it is very likely that someone is going to have to poke a hole in your ceiling to find the problem. However it is most likely to be his pipe leaking - not yours.
Is it on a potential route for either water coming in, or more likely a sewage run pipe on its way out?