While Finch enquired about what happened in the detention centre in V for Vendetta, they came to realise that the priest was the highest paid staff there. But eventually I think it's not clear why they needed a priest in there.
The article on the priest (Bishop Anthony Lilliman) over at the DC Comics Wiki provides some answers:
Lilliman was the chaplain at the Larkhill Detention Center and was tasked with monitoring "rules and rights" violations. However, his £200,000 a month payment kept him silent while Commander Lewis Prothero and others worked on the St. Mary's virus, which the fascist government, Norsefire, used to kill thousands of people.
I can't remember from my reading of the graphic novels how Lilliman came to be at Larkhill, but I think the implication was that he was assigned rather than chosen to be there.
Therefore, he was given an extremely nice slice of money to effectively keep this mouth shut on any violations. That explains the highest paid staff part (although I had a quick browse through the script and didn't see that part anyway - if you can remember when it was said, do comment!).
Finally, the reason for him to be there, officially, was to look after the "rules and rights" of the centre and the prisoner and to provide spiritual assistance to any of the children.