I have only just noticed your posting. I can confirm there is considerable mention of the Annetts in Pam Cogell's book "Collingbourne Remembered", particularly pages 117-122 which traces the family history from William in 1731 to Reg who died in 1992. There are several old phoptographs of the family. I do not see specific mention of your Charles, so they may have been a parallel line.
I am aware there were several Annetts lines in the district and one, William Henry, married into my own family to Fanny Walker in 1895 in Collingbourne Kingston. CK and CD are only 1.5 miles apart and are very closely associated.
If you have a James or Arthur Annetts in your line during the latter 19th century you may be a descendant of John and Francis West. In this case that could be another source of considerable information.
I hope this helps.