Burwell 1851 is lost, and is most unlikely now to be found, so that's water under the bridge, albeit frustrating!
So what firm facts do you have:
Charles H Barnes was baptised in Swaffham Prior in 1837, son of Ann (per baptism index on the Cambs FHS website
http://www.cfhs.org.uk/Search.html). Swaffham Prior and Burwell are only a mile apart.
John C Barnes, base born son of Ann was baptised in Burwell in 1834.
Do you have baptism details of Charles' mother, where hopefully you'll pick up her parents and possibly her father's occupation? (on the same baptism index there's an Ann baptised in Burwell in 1810 daughter of John and Sarah). John and Sarah appear to have been the only Barnes family in Burwell judging from the baptism index.
Have you found Ann, Charles or John in 1841. I can't see them in Cambs (although there is a John aged 7 in Swaffham Prior living with Henry & Elizabeth Downham, both aged 60. But there is another Barnes family in Swaffham with young children so he might be one of theirs)
Turning to the Ann who married Matthew Bowers in 1847 in Burwell, was she described as spinster? Matthew presumably was a widower? The IGI shows her father as John - what was his occupation as shown on the marriage certificate? Does it correlate with the John, father of the Ann christened 1810? Unfortunately her age (as shown on the IGI marriage entry) of 33 doesn't match the 1810 christening, but she wouldn't have been the first person to have been economical with the truth with marriage ages!
Who were the witnesses on the marriage cert? Are there any clues there?
Have you traced Ann's other two illegitimate sons? Sometimes looking laterally can help. Did they name a father when they married (a stepfather's name is sometimes seen)? Who were the witnesses at their marriages? You need every scrap of information you can find!
If it's not the same Ann Barnes there are an awful lot of coincidences, but proving it is another matter, particularly without the benefit of the 1851 census.
Was Matthew also dead by 1861?
When it boils down to it this is one of those nice to know, as opposed to need to know, facts! You know Charles mother. You know Mary Bowers' parents. You know, or can find out, when her mother died. It's just nice to know that her father married his mother! And as far as I can see marrying your step sister was not one of those banned relationships.
Hope this helps
Regards
David