Senior pastor at Charlotte Chapel Baptist church, Paul Rees has been campaigning against any proposed changes to the status quo. Speaking to Premier, he said: "They're going to do a study of who comes into the city centre and what their purposes are on a Sunday and then they're going to come back with some specific proposals.
"There's no definite plans yet but obviously showing keen interest to restrict the amount of parking that happens on a Sunday here in Edinburgh."
However, some councillors have voiced also concerns that protecting Sunday parking in response to a plea from church leaders could breach equalities legislation.
According to the Edinburgh Evening News, deputy transport convener councillor Adam McVey said: "I think it's worth mentioning that we're a secular city.
"No religion has a hierarchy in terms of making representations and the effect that has on our policy making."
The council says there are currently no proposals to introduce charging on a Sunday but increased parking controls on Sundays is something it is "exploring" as a means of potentially reducing traffic, improving the environment for pedestrians and cyclists as well as increasing turnover and footfall for businesses in the city centre.
Paul Rees, senior pastor, Charlotte Chapel Baptist Church: