My Great Grandfather was Edward McDermott who lived in Shercock in c.1840 where he married my Gt. Grandmother Bridget McEntee in 1840. They had 6 children that I know of, the first one was a Mary in 1842. The 2nd one in 1843, a boy, who was named 'Michael'. Other children were James, John (Thomas), Edward, Patrick, Annie.
I have traced Bridget on the 1881 English census as living in Durham with Edward, Thomas and Annie. The other children of this family, including Michael, stayed in Ireland as far as I know.
They may have been already married when their mother left Ireland and didn't want to emigrate. Patrick did go to England but returned to Anaherin in Cavan.
I'm wondering if perhaps these remaining children, or Michael, may have married and named their first child Michael, raising the possibility of it being your Gt.Grandfather. The Michael of this family would have been 26 at the time of your Gt.Grandfather's birth, so is a possibility.
T