And with an uncommon name like Herbert Wiggins, you should find the family easily enough
1901 14 Paget St, Penarth RG13/4989 folio 10 pg 11
James E Wiggins head mar 43 foreman Taff Vale Railway b. Cardiff
Emma wife 44 b. Devon, West Down
Henry E son 22 assistant foreman ship broker(?)
David son 20 coal trimmer
Ethel dau 17
Baetrice dau 16
James C son 14
Herbert O 12Ivor son 10
May dau 4
Ralph son 3
Gertrude dau 1 yr 4 months
all children born Penarth
Do you have your parents' wedding certificate? This would confirm her father's name.
If you have access to the census online, you can then trace the family back through the years, getting marriage and birth certificates to confirm your findings.
Or you can ask for look-ups on this board.
If this is the correct family, your best bet would probably be to get used to searching with the Wiggins family as there are some good names there to help you get back further.
Then, when you're feeling very brave, and you have confirmation of Elizabeth Thomas as your grandmother and her father's details, you could attempt the Thomases. I have a family of Thomases in Cardiff at this time, all with common first names, and I've only managed my direct line as the marriage was to an uncommon surname. The others are a bit hit and miss.