Have found a more plausible entry for "my" John Thomas in 1851 living at Upper Water Street, Llanelly (H0107, Piece 2468, Folio 242, page 21). Born abt. 1800, therefore doesn't look like yours Tegan but still may be the same as yours English Daisy?
A Carpenter (same profession as his father) born St.Clears Carmarthen abt. 1800, (his parents Jonah and Elizabeth had moved to Llanelly by 1806 as next child I know of (Elizabeth) was born in Llanelly in 1806). He was living with his wife Elizabeth (56), son John Thomas (21) also a Carpenter, dau Ann Thomas (15), dau Martha Powell (nee Thomas) (24) Widow and a Grocer, grand dau Elizabeth Powell (1), nephew, James Davies (19), servant Hannah Thomas (23).
In 1841 was listed as just living at Water street with his wife, dau Ann (6), son John (12), and dau Martha (14) (HO107, Piece 1379, Book 6, District 7, Folio 9, Page 10, Line 12).
By 1861 it looks like he was living as a lodger at Park Street (formerly Joiner with no mention of his wife or the rest of the family (RG9, Pice 4112, Folio 46, Page 37)