If the housebuilder refuses to rectify snagging in the 2 year warranty period, you should write to the NHBC. It has a dispute resolution (not much good but better than nothing) and they can instruct the housebuilder to do the works by a certain date and, if they don't appoint another builder to do it.
It is common practice to grind down new homeowners as most give up at around 18 months - 2 years anyway. Until a new homes ombudsman is created by government buyers don't have much they can do other than go to court.