Family of Patrick W. Burke b. 17 March 1852

I'm looking for information about my great-grandfather Patrick William Burke, his birth parents and their families. I have quite a bit of information from Ancestry, so I'm looking for more local knowledge and records. According to Patrick's death certificate (14 January 1916), Patrick and his parents Jno. Burke and Winifred Burke (nee McDermott) were born in Ireland. Several published death notices indicate that Patrick was born in County Mayo, although this information is speculative at best.

I have a number of other records from Ancestry that indicate Patrick was more likely born in England, perhaps due to his parents emigrating to England during the potato famine. This other information also indicates that Patrick was raised by Winifred and Jno. (or Owen) Gigalon (or Kilgallen). The most likely scenario is that Winifred re-married Gilgalon/Kilgallen. I have a record from Roots Ireland showing their marriage could have occurred in 1855 near Kilbeagh/Charlestown in County Mayo.

There may be other plausible explanations of  Patrick's relationship to the Gilgalons/Kilgallens. One possibility is that both of Patrick's birth parents died and he was raised by the Gilgalons/Killgalens. In any event, Patrick retained his Burke surname throughout his entire life and I'm fairly certain his birth parents were both born in Ireland.

I have personal DNA results from Ancestry that show I have family connections to the Province of Connacht, particularly in the region of Connemara. While this may be attributed in part to my mother's side of my family, the connection is very strong, which suggests this area is very likely where the Burke family lived. 

Any insight is appreciated.