I know exactly how you feel, as I've been going through noise issues too (at my student apartment and my office space at uni).

I wear earplugs (the disposable kind). This does get me looks from people who sometimes pass by my desk. I have also tried ear muffs (the type one would buy from a hardware shop). Unfortunately they are not comfortable, especially when you wear them for a long period. I have also tried headphones over ear plugs, which does work temporarily. But I found that no matter what you do (ear plugs, soundproofing), one will find the muffled noise infuriating. I found myself actively listening for any noise whilst wearing my earplug/headphone combination, which sort of meant that I wasn't concentrating on my work.

What I have found is that while these provide temporary relief and some sanity, nothing is better than to go to higher authority. It is worth notifying the offending people of their problem, but sadly I don't think it will change the situation much. Even if they think they are being quieter, they will still be too noisy. If confronted, they might even retaliate (by being noisier) if they are that immature. I think it is better to notify the higher authority notified first of the issue. Emailing their office sounds like a good idea... so it becomes more like a general complaint.