English marriage and death certs do not give place of birth.
I'm afraid this is incorrect. On English/Welsh death certificates from 1969 onwards there is provision for stating place and date of birth.
What Bookbox says is true; unfortunately foreign births are only recorded by country, not by town/city, so the death cert will only state Poland.
What was Bronislaw's father's name? You should find it on his marriage certificate. I ask because there are time restrictions, usually 100 years, on Polish BMD records, and it may be easier to search Polish records for his father.
Did he have siblings who came over here as well or to the US? Did he remarry in Oldham?
Kind regards
Gaie