The generally accepted source for information about what Roman Catholic parishes were where and when in England (and ?) is
"Catholic Missions & Registers 1700-1880", vol. 1-6;
Author: Michael Gandy
Published London : Michael Gandy, 1993
I don't, however, have access to any of the volumes for that part of the world.
Online information is generally to be found in the GENUKI system. See the GENUKI Gazetteer. There are pages for Holborn St. Andrew, St. Giles In The Fields and Bloomsbury, which may or may not be the (Anglican) parishes that you need. None look especially fruitful, with only 2 RC parishes listed - founded in 1873 and 1853. You are therefore probably going to need to look wider afield in the GENUKI pages for Middlesex to see what RC churches are in the surrounding areas. I don't know of any simple way of finding references to RC churches other than checking each (Anglican) parish manually. I think it's just hard work with maps and the gazetteer.