Jenni, more likely that the Thomas's just took Charles in. I think it wasn't until the 1920's or 30's that official adoption took place.
I can understand being unable to find Elizabeth in the 1891 census as she may have married or died, even though you have found evidence of neither, but she must be somewhere on earlier censuses.
If we
guess that she might have been in her late teens to early twenties in 1886 when she had Charles, as a rough guide she
may have been born some time between 1850 and 1863. This doesn't really help if we can't find any Elizabeth Plaws.
Although she had Charles in Chester, she could have been born anywhere - maybe sent to Chester to give birth.
If you have a look at google maps much of St Anne Street has been 'developed' but there are some old terrace houses with numbering around 128 (but these may have changed over the years) - it's just interesting to see them. (I checked in case it was an unmarried mother's home or similar).
Does anyone know how to check who was living at that address in 1881 and 1891, in case it was a family member of Elizabeth?

Jenni - do you have Charles marriage certificate? I don't suppose he gives a father's name?
