Hi,
SNAP !!

If the Wiltshire Charles Hatter is the correct man then you can narrow his immigration down, he appears on the 1871 census boarding with a James and Jane Farmer. Anc* have him transcribed as Hattel, it is clearly Hatter on the image, plus a few doors away are William and Mary Cottle
Westbrook, Bromham
Charles Hatter 22 unm ag lab bn Wilts Bromham
Class RG10, Piece 1913, Folio 60, Page 11.
So he must have left England between 1871- 1876
Hope this helps
claire