Sorry for the lack of response, it was the last strand on my family tree in trying to go back another generation. After the first response, I concentrated on writing up the information I have. Also, I did not receive any notification of responses, which I need to address. I appreciate within formal documents the truth may not be recorded, false information was given, which has been the case throughout the generations. As the birth is before formal records, I now do not feel the answer will be found. Thank you for your responses.
He was Welsh. His name being Thomas Williams and according to the marriage certificate (1855) his father was John a labourer. Without pin-pointing a year, it is impossible to find a Thomas Williams in West Wales as the dates say between 1834 and 1838. Two census records say the later. I asked because his age being noted as full. If that was 21, it would suggest a birth year of 1834 or before. The other issue is that he was born in Newcastle Emlyn, which borders different counties that changed it boundaries over time. One census says Newcastle in Emlyn, Cardigan. Born in Newcastle Emlyn seems consistent.
I looked at his wife Margaret Howell and the census dates are just as vague and there are more of census records. But I have a christening that notes her date of birth as 19 Jun 1834. He was a mariner/labourer depending on the census and at the time there was plenty of freight by sea, so I assume he was away for certain census dates. I have him in 1901 living in Llanelli (b. 1838) and working as a Navvy having separated from his wife. By 1911 he was in the Union Workhouse in Llanelli (b. 1835).
For Laugharne the 1861 census is missing, which could have answered so much. I can find her still with family in 1851, but not Thomas Williams, though he could be working/living anywhere. And nothing for him in 1841. He may be recorded on both, I simply do not know where.
Added: Witnesses of the marriage were her father Jonah Howell and Jane Killa, who I believe ran a public house; both locals to Laugharne.