Hi,
I'm not sure if I am looking at the same image as you, I see Robert's name as Robert William Wake, son of Robert WHEATLEY,
http://www.rootschat.com/links/01u8a/I can't find Annie Gertrude's or Elizabeth's births but I have found the other grand-daughter Emily,
Bailiwick Of Guernsey, Civil Births
02 Apr 1864
Emily
(illegitimate)
Mary Ann WHEATLY
Birth place Grande Rue
That's the same address the family is at in the census, Robert Snr and Mary have a daughter Mary Ann b.1841 living with them in 1851
As Emily used the name Robert as her father when she got married it seems that she was actually using her grandfather's name. I wonder if the other girls did the same?
Daisy