Interested in better understanding of Irish immigration to England early 1800's

My cousin and I have a DNA connection to a Houghton family from Ireland who immigrated to greater Manchester by 1823.    Their eldest son, Charles, was born in Ireland abt 1819.  My Haughton/Houghton family have been in Cloonboygher since at least the late 1700's and remain in the area still.   I'm trying to figure out if  the family that immigrated were from Co Leitrim as well.  The parents were Thomas and Margaret Houghton and are verified on their English born children's baptismal, marriage and death records.    Charles lists Ireland as his place of birth throughout his life.   Their son, Henry, may have been born in Ireland as well.   Unfortunately I can find no other records for the parents.   

Is anyone able to check the 1821 census fragments for a Thomas Houghton in Cloonboygher (or Co Leitrim), a marriage record for Thomas and Margaret or possibly a baptism record for Charles?    

It's been interesting following all my granny's DNA back to Lancashire.   Someone mentioned to me that Lancashire supplied military to "subdue" Co Leitrim.   That just hurts.   Is their any historical substance to that?  I know they were planters but I would like to think they were all as kind and loving as my dear granny and her sisters.   sigh 

Thank you so much for your input,

Marylou