The marriage certificate arrived: 22 Dec 1855 in the Parish Church of Laugharne. It names John Williams as the father and was signed in the presence of Jonah Howell (her father) and Jane Killa, both with a cross. Rank or Profession of Father, gives Labourer for both. I assume his father was not present, with Jane Killa as witness. In 1871, Jane Killa was a Licensed Publican.
It is like searching for the needle in a haystack, looking for a John Williams in West Wales. The census information suggests his son Thomas was born c.1838 Newcastle-in-Emlyn Cardigan.
On Family Search I found a John Williams born c.1806 in Newcastle Emlyn, Cardigan on the 1861 Census. Registration Number RG09 Piece/Folio 4138 / 40 Page Number 15: Mary Williams his wife, born c.1803 in Llanstephan (Llansteffan) with children James Williams born c.1835 and Hanah Williams born c.1843 both in Llanstephan. Llansteffan is just around the headland from Laugharne. Thomas Williams was born c.1838, which fits within this the dates of this family. Although Census information says Thomas Williams was born in Newcastle Emlyn, they could have moved to Llansteffan after he was born and before James was born. It seems too close to be coincidence. At present I cannot find anything on the 1851 Census, which could confirm or dismiss my hunch.
Any ideas on this and what I do next?