A branch of Annetts from Collingbourne Wiltshire moved to Wales in the middle of the 19th century. They seemed to spread out across south wales, from Porthkerry near Barry. It is possible that your family could be linked to these. My great-great-great grandfather William (1815-94), born in Wiltshire, lived for a while in Porthkerry, before moving to the Pontypool area with his sons George and Thomas (my great-great gfthr). A family of Annetts can be found still living at Porthkerry in the 1881 Census. (George and Mary Annetts + 7 children). I hope some of this may help.
Thomas whilst in Trevethin, Pontypool married Elizabeth Evans, dtr of Charles, and they had two sons, one of which was my great grandfather Thomas Edward (born 1888). He married Emma Yorke in 1907, and moved to Nelson Green in the Forest of Dean. A lot of my family come from here, including my grandfather Clarence, and my dad Terry. If anyone has any connections to this branch, please post a message. Thanks. (My name is also a Thomas)