It is not mentioned in the article, but a part of the reason for the dramatic increase in the "No religion" category is that in the 2016 census, the "No religion" option was the first option in the list of religions. In the past, it was always the last listed option. That factor probably added 1 or 2% to the category.
From memory, the census doesn't break down different types of Muslims. There is just one overall category of Muslim, which is a weakness in the census in my view.
In relation to steve2's question, I have all that data and more, but I can't get to it for the next few days. If you look through my old posts of about 8 months ago, on a thread started by sbf, you will find it. I am planning to write a little piece on it all, next week.