I'd suggest starting the search with Edward junior - do you have a baptism record for him already ?
The 1851 English census gives his place of birth as "Dublin, Kingstown" which is now Dún Laoghaire, I see a possible match for Edward's baptism in Catholic records for this parish on the 20th May 1849 to parents Edward and Mary Evans, see about one third down the right hand page, which could fit as his age is shown as 2 years on the 1851 census. Unfortunately there's no mother's maiden surname recorded, which could fully confirm the match, but this does fit the clues we have..
Have you located Edward senior on the English census, do you know where he was born ?
I'm wondering he he might have been Church of England which would probably mean that their marriage would have been mixed and taken place in a Church of Ireland..
Catholic baptism records for the parish of Passage West, Co. Cork go back to about 1795, and these include a baptism for a Mary Finton on the 16th August 1818, to parents Tom Finton and Mary Tuomy - see 5th entry near the top of the left page
I found a number of other Finton/Fenton baptisms is the parish during the early to mid 1800s but no promising matches for John with the same parents. The images of the registers for the parish for the 1810s and 20s on the NLI website look fairly complete so might be worth a detailed browse of the images to see if there's any sign of a baptism for John
