well, the tower was a castle first, royal residence...
BUT...they always had those little chambers in the basement the content of which was often forgotten...not just in the Tower of London...a rather universal thing....monestaries and convents were another place where you didn't want to be against your wishes...
My other half has done Public Duties in the Tower (means he did the guards there) and there are no dungeons, the rooms are all in towers and in the main buildings. It was a proper castle not a prison. It was first used to house prisoners by Henry the Eight, including his wives.
Yes we have plenty of Catholic chapels in Yorkshire including one in Middleham by Richard's castle. We have the ruins of several magnificent abbeys here, destroyed by Henry the Eighth, he also massacred many in the North.
http://suite101.com/article/the-pilgrimage-of-grace-a113234
Robert Aske came from a couple of miles from where I am and his home Aske Hall is still standing though with improvements made over the centuries, one tower has been untouched though since 12th century.