Hi Thindle,
I think I have found the family in 1861 (indexed as Moren) as follows:
James (not John) Moran 40 Ireland
Bridget 32 Hull York (not Ireland)
Mary 14 Hull York
Henry 12 Hull York
Andrew 6 Hull York
Helen 4 Hull York
I also found an IGI reference for James Moran marrying Bridget (no surname) about 1848 Shipley Yorkshire. Unfortunately, there is no mention of Bridget's surname.
Cheers, Colin