BMD index for England has the following people listed on the same page......
View Record Name Year of Registration Spouse's Surname District County View Image Order Record
View Record
Catherine Curphey 1845 Wirral (1837-1974) Cheshire
View Record
John Downes 1845 Wirral (1837-1974) Cheshire
View Record
Hannah Griffith 1845 Wirral (1837-1974) Cheshire
View Record
Elizabeth Redford 1845 Wirral (1837-1974) Cheshire
View Record
Thomas Smith 1845 Wirral (1837-1974) Cheshire
View Record
John Wattleworth 1845 Wirral (1837-1974) Cheshire
----so the most likely mother of John Robert Wattleworth is Catherine Curphey, since the 1861 census says she was a Catherine from the IOM, and Curphey is a Manx name.
The marriage was in the first quarter of 1845. This is consistent with the oldest child being 15 in 1861.