I'm afraid my research on the Acton side hasn't got very far this year. I was hoping to go to Ireland but I still don't have the leads or the time out from work to make that trip.
I know for certain now that my great great grandmother Bridget Brannan's family were from Ireland and she married an Acton, but John (her husband) was the illegitimate son of Martha Acton and took her name.
The name of Robert does come up in my own family tree. Ellen, my great gran, had a younger brother named Robert (b.1886) and Martha (my gx3 grandmother) also had a brother named Robert who was born in 1821 (although he died and was buried in England in 1878). His father was Thomas and I suspect that Thomas was the son of one William Acton, but so far as I know these people all lived and (apart from William, about whom I cannot be sure) were born in England. William or Thomas may have had a brother named Robert but I cannot find any record of him.
John and Bridget, my great great grandparents were married in Wigan in 1860, which also suggests a familial link.
I have not given up on this branch but I do need to take some time off to do more intensive research. I will not fail to let you know if I discover more.