I have two John Garrity/McGarritys that might be of interest. The first was born in Ireland but left in 1860 with his wife Bridget Diver to settle in County Durham England.
The second is an uncle, the son of Thomas Garrity, also born in Ireland. John was born Feb 25, 1882 in Chapel Street, South Hetton, County Durham.
All the family, great grandfather, grandfather and aunts and uncles used the names, Garrity, Geraghty, Garraty, McGarrity throughout their lives. Grandma Sarah Jane Martin hailed from Co. Tyrone and I think Great Grandfather John (Sean) may have lived there for a few years before leaving for England. Prior to his stay in Tyrone he lived in Co. Mayo where he was born and married Bridget.
Most were coal miners until the early 1900's. Check out the coal mining district of Co. Durham, England. There were other McGarrity's living there in the mid to late 1800's. Some of the coal mines my kinfolk worked at were Trimdon, Murton, Wrekenton, Gateshead and Westoe, all in Co. Durham.
They were all Roman Catholics. In church records their name of choice was McGarrity. Did they know the history of the name and its origin Mag Oireachtaigh? Or perhaps the parish priest was Irish and knew how the name evolved.
If you need a good family historian who is familiar with the district and McGarritys who lived there in the 1800's, let me know. I have a contact who helped me gather my genealogical data and is very reasonable. He's thorough and really knows his stuff. He may even have some data in his files on your kin already.