Hi Margaret,
Yes, I see what you mean.... bit tricky this one isn't it? You'd think with a name like Axelina it would be easy to find them, but I've tried all sorts of variations, but come up with nothing.
I found James and Axelina's marriage in 1876 (Apr-May-Jun) in Greenwich. This gave me James Carod Chesterman marrying Axelina Matthews in Greenwich.
After that I looked for deaths and re-marriages. A couple of minor possibilities only:
1. *in_ (as transcribed) Chesterman marrying either William Mellowship or James Nevill in Jan-Feb-Mar 1886 in Bethnal Green. However the index page gives the name as "Letina", and no children's names matched with surname of Mellowship on the 1891 census.
2. There is a death of a James Chesterman in Greenwich in Oct-Nov-Dec 1881, but his age is transcribed as 78 !! Unless an error, not your man, but maybe a relative?
I've looked to see if James and Axelina were living with any of their Matthews family, but nothing jumped out. I've also looked for each of the children and for anyone born in their times in Bermondsey. I've also played about with wildcards (ie Che*, etc).
I'm sure someone will come up with something I've not thought of or by using better search criteria.
Have you checked whether they emigrated? Maybe a posting on the London board might prove more fruitful?
Sorry I couldn't be more help,
Sally