My great grandfather, Joshua ACKROYD had a brother called Benjamin ACKROYD who was born about 1842 in Bradford. Benjamin appears in the 1851 census with his family & I have not found him again until the 1881 census when he is with a wife, Mary & son, Isaac aged 8. Obviously this is a hunch but he is the right age in the right place & is a stonemason like his father & 2 brothers.
FreeBMD has a marriage with Mary HEATON in the June quarter 1876 which fits & there are a couple of patron submissions on the IGI which relate to this marriage.
In 1901, Mary appears as a widow (there a possible death for Benjamin in 1893) & Isaac is a 'Butchers Meat Salesman'. FreeBMD has a possible marriage in the June quarter 1902.
An Isaac of the right age appears on the Ellis Island database in February 1912. He is travelling with a son, Edgar who is 8. He says he has been in the USA previously from 1905 - 1911 & is returning to Sarles/Surles. Here the trail goes cold. Neither appear on the SSDI though there is a much younger Edgar AKROYD. Ancestry has a reference to an Edgar AKROYD in the 1920 census but I don't have access to that.
I'd love to be able to contact who ever put the references on IGI & of course anyone else who knows more about this family.