The IGI has a baptism of Archibald Angus Campbell, father Neil, mother Annie, in Whitewell, Derbyshire on 30 December 1873. This matches a birth in Runcorn in the September quarter of 1873, reference Runcorn 1873/Sep Qr/8a/221.
You need to get that birth certificate to get Annie's maiden surname. Then you will be in a better position to look for the marriage of Annie and Neil, which will confirm at least the name of Neil's father.
In 1881 they are in Derby, Neil and Annie both aged 33 and born in Scotland, and eldest child Neil aged 9, born in Chester. This matches a birth in Chester 1871/Dec Qr/8a/350.
There is no marriage of a N*l Campbell to an Ann* in FreeBMD before 1871.