On 1901 census, 8yr old Mary Ganley was living with her parents, "Bartholmew" age 42 and Alice age 27, and siblings John and Jane (aged 10 and 3) with many other families at 37 George Street, Sunderland. The whole family were born in Sunderland and Bartholmew was an ironworker.
If the Irish connection was with this family, it looks like they left Ireland before about 1860.
Because Kelly is such a common surname, you would probably need to buy the correct wedding cert to be sure of Thomas's father's name, then see if you can find him on the Irish 1911 census (free) or English/Welsh 1911 census (pay to view) and take his story back from there.
If you decide to buy certificates, do so from either the Sunderland Register Office (for these certs) or the GRO
www.gro.gov.uk - where they will cost about £9 each and not through organisations you find on the net which will charge you much more