Well, it appears that we are related..... I am a descendant of Augustus Radcliffe via Joseph Bailey Radcliffe, Mary Allgood Radcliffe's brother. All of these posts have provided me with quite a bit of new info, which I'm going to be studying closely. At any rate, you might look for Mary's birth records in Wales. The 1861 census shows her other brother's (Alfred) birthplace as Swansea, Glamorgan, Wales.
I'm afraid that I probably can't help too much more on Mary (as yet), since I only discovered Mary, Emily and Alfred when the 1841 UK census was released. There must be some kind of IOM connection though, as Joseph attended school there and I've wondered about that since the family was living in Lancashire.
Get in touch with me if you want to compare notes. BTW, Joseph ended up in Canada and his
widow & children in Minnesota. Guess we're a far-flung family!