They are definitely called Cooke ten years earlier ...
1851
Wolstanton HO107/2002 Folio 220 Page 35
William Cooke Head M 24 ? Engineer Cheshire Barthomley
Olive do Wife M 20 Stafford Wolstanton
Kidgrove (?), Wolstanton
In the last quarter of 1849 there was a marriage at St John, Goldenhill between a William Cook and an Olive Chadwick, which might be relevant.
posteria
ps I cannot read the word preceding "Engineer" for William but he is, without doubt, an Engineer of some kind.