Possible marriage into Cummins c 1830s?

[ThrelfallYorky]

I've got a long-standing problem that I'd welcome advice on.
I have a Thomas Cummins, born 1814 -18 in Ireland, who marries a Mary ? also born 1814 -1818, in Wexford, according to later English censuses.
Their children are John(b1834), Elizabeth(b 1839/40), Thomas (b 1842ish), and Johanna(b 1844 Wexford). As Mary gives Wexford as a place of origin, and Johanna appears to have been born there, where could I try to find what Mary's maiden name may have been?
Any advice would be welcomed.
I've posted before about young Thomas, but been totally unable to get any further with his lineover a few years, and wonder what the chances(!) will be of tracing the maiden name of the mother of those children, linked to that father? My Irish ancestry is proving totally elusive to date.

[Maggsie]

Hi,
Where in England did they live?
I have looked for Johanna in Ireland records, no result.
Maggsie

[ThrelfallYorky]

They seemed to arrive at Liverpool, they were there by the 1851 census.
I lose the parents after 1861 census, but the children seem to have moved to Bolton, and one later with his family to the Southport area of Lancashire.
I've always assumed they were poor Irish peasant forced to leave because of the situation in Ireland in the 1840s and a little later, as children listed were all born in Ireland.