Hi sorry to hear of your trouble, I know how irritating noises can be...
I've done a bit of sound proofing in my house and spent a bit of time researching it.
Your new build will have had to comply with Part E regulations - the pdf doc in online (google it). From what i remember the 'compliance' is more about building to a certain 'standard' and i think in only around 10-20% of cases the actually installation is tested. From memory I think the regs call for around 45 dB reduction from a party wall, and this should have been satisfied by the developer with the appropriate methods, although I wouldnt be surprised if things have been short cutted!
You have a few options.
1. Pursue the developer and try and get them to fix it. You would have to demonstrate that the regs were not complied with to get him to do anything here - ie some form of testing, or if the show that the wall hasnt got the right standard here.
2. Upgrade the soundproofing yourself.
The following may sound obvious but anyway its worth remembering that the best reduction in sound will come from the source - if your neighbours have little in the way of acoustic damping, ie little furniture, laminate floors etc, then the noise they generate doesnt get damped at source (think bathroom acoustics).
Upgrade wise there are a number of options - I assume that your adjoining walls are plasterboard studs - there should be the approriate sound insulation in there - you say that it is a cavity (just re read) which is probably where you can get the most help here. I am surprised that there is no insulation there!
1. Upgrade insulation with acoustic mineral wool, then fit 1 or 2 layers of acoustic plasterboard with staggard joins (this is heaver than normal stuff)
2. Upgrade with insulation and resilent bar system. - These bars effectively decouple your wall from the stud to help prevent the transfer of sound.
On the websites below I think they give you an idea of the amount of dB you can get for each solution. IRC standard 12mm plastboard stud only offers around 20-25 dB reduction, which is f all.
In anycase, to stop sound you need mass. Foam will not help. There are a number of firms that could advise better than me, as i effectly got my knowledge from google and others! But is sounds as if a mineral wool and plasterboard upgrade would probably help.
http://www.soundstop.co.uk/
http://www.keepitquiet.co.uk/
etc.
hope this helps,
Andy