The position that opposes disestablishment is Antidisestablishmentarianism. The term was never common but was occasionally used in debates in Britain in the 1860s about the official status of the "Church of Ireland", which was a Protestant church and was closely associated with the Church of England. It was disestablished by the British Parliament in 1871--that is, it continued to exist but no longer had the status of an official government-sponsored church.
There never was a question of disestablishing the Church of England in England itself.
The word is famous because it's the longest ordinary word in the dictionary.