Possibly odd for a lot of people here, but I have in fact identified my first non-English ancestor - or at least confirmed that she was actually born in Ireland as previously this was just assumed.
I have her in England on two censuses. From the birth of her eldest child, she must have been in England since at least 1891 (although not identified on that census). She was born round about 1865 in Tralee, Ireland and her father was called John Kenny. I have his name from her marriage certificate. She doesn't appear to have married the man she lived with for many years and who fathered all of her children, even though she gives her surname as Wright in the 1901 census. The certificate of marriage for her later partner does give her condition as Spinster, but I presume he knew about the family! Arthur George Wright appears to have disappeared back to Norfolk to live with his twin sister and her family. No idea what happened. My guess is that they didn't marry originally as she was Catholic, but that's just a guess and her 1906 wedding was CofE. Maybe she overcame her scruples!
That's a fair bit of background, but what I really would like help on is knowing where to look next. I'm guessing she didn't come over on her own and imagine it was the lure of work but I'd appreciate any help on where to look for possible shipping lists and where to look in the Irish records. I know they can be a bit patchy.
Based on the names of the children, I have a slight inclination towards her mother being a Bridget, but father being one of a multitude of Johns isn't much help!