That is interesting Wilcoxon as I noticed what appeared to be the right William Edwards in later census returns but married/living with someone else.
The 1871 has William Edwards in 20 Bryn den Gurnw (?) Ysceifiog aged 60 and with Anne, wife, aged 49. This suggests to me that it was a second marriage at least. They have a son David Edwards, unm, aged 21, born Ysceifiog living there too. This appears to be the same place in Ysceifiog, Bryn.... that William was living in the 1851 census. RG10/5642 Folio 57 Page 4.
In the 1861 census, William Edwards, age 50, is living at 40 Brynden.....??, Ysceifiog, with Ann, wife, aged 44. They have others living with them shown as Lebbeus Jones, unm, age 19, Son In Law, Agricultural Labourer and David Jones, age 9, Son in Law, both born Ysceifiog.
David's age more or less agrees that with David Edwards, Son, in the 1871 census. Did he change his name to Edwards?
There is a couple on the 1881 census, William Edwards, age 68, born Ysceifiog and Anne Edwards, age 63, born Denbigh. The ages have wandered a bit but I suspect it is the same couple.
The maiden name of Anne appears to be Jones from the details given for the two people shown as Son in Law in the 1861 census. Marriages for William Edwards to Anne Jones on BMD are in the December quarter of 1855 in Holywell RD (a bit quick) but North Wales BMD shows this marriage in Ysceifiog, St Mary, so it looks possible.
Jo.