If you know the name and occupation of Mary's father it might be possible to locate him on the 1911 Census, if he was still alive. I had a look at the marriage index details posted in the other thread for Patrick Kane & Mary McCarthy - but it does not seem to be clear as to her fathers name ..also the source or type of record is not mentioned.
A civil cert would give you these details, which would help to narrow down the correct family. Assuming Mary was living at home with her family in 1901 it may be easier to find her on that census. The details for that census are due on the National Archives website early next year.
Shane