when I started working in my current role thenotice period was 1 month. Now I have learned that due to some changes the notice period has been increased to two months.
Precisely. It matters not what the current terms a new person might be employed on. What matters is the basis on which you were taken on, plus any changes that may have been agreed with you since.
Again, check your contract. In many jobs people leave without serving their notice - the company can sue you for breach of contract but is unlikely to do this . I did this with a private company and had no comeback - apart from bad feelings, which didn't bother me because they'd treated me shoddily! (although with it being an organisation as big as the NHS, I wouldn't count on this!)